BIBDs with v = 16

Cyclic or 1-rotational BIBDs with v=16
v b r k Found Comments Where
16 30 15 8 24 here
16 30 15 8 1 Resolved here
16 40 15 6 20 here
16 48 15 5 198 here
16 48 15 5 4 Near-Resolved here
16 60 15 4 402 here
16 60 15 4 Resolved
16 80 15 3 69 here
16 80 15 3 120 Near-Resolved here

Now follow the results of searches based on various groups of order 16. Two of these are essentially the Galois Fields GF(24) and GF(42).

Group 2: abelian, with relators: {a2c-1, b-1a-1ba, c-1a-1ca, d-1a-1da, b2d-1, c-1b-1cb, d-1b-1db, c2, d-1c-1dc, d2}.

BIBDs with v=16 for group 2
v b r k Found Comments Where
16 48 15 5 33 here
16 48 15 5 Near-Resolved
16 80 15 3 21 here
16 80 15 3 Near-Resolved

Group 3: non-abelian, with relators: {a2d-1, b-1a-1bac-1, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2, d-1c-1dc, d2}

BIBDs with v=16 for group 3
v b r k Found Comments Where
16 48 15 5 33 here
16 48 15 5 Near-Resolved
16 80 15 3 10 here
16 80 15 3 Near-Resolved

Group 4: non-abelian, with relators: {a2d1, b-1a-1bac-1, c-1a-1ca, d-1a-1da, b2c-1, c-1b-1cb,} d-1b-1db, d2

BIBDs with v=16 for group 4
v b r k Found Comments Where
16 48 15 5 14 here
16 48 15 5 Near-Resolved
16 80 15 3 23 here
16 80 15 3 Near-Resolved

Group 5: abelian, with relators: {a2c-1, b-1a-1ba, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 5
v b r k Found Comments Where
16 48 15 5 60 here
16 48 15 5 Near-Resolved
16 80 15 3 42 here
16 80 15 3 Near-Resolved

Group 6: non-abelian, with relators: {a2c-1, b-1a-1bad-1, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 6
v b r k Found Comments Where
16 48 15 5 115 here
16 48 15 5 Near-Resolved
16 80 15 3 46 here
16 80 15 3 Near-Resolved

Group 7: non-abelian, with relators: {a2, b-1a-1bac-1, c-1a-1cad-1, d-1a-1da, b2, c-1b-1cbd-1, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 7
v b r k Found Comments Where
16 48 15 5 99 here
16 48 15 5 Near-Resolved
16 80 15 3 5 here
16 80 15 3 Near-Resolved

Group 8: non-abelian, with relators: {a2d-1, b-1a-1bac-1, c-1a-1cad-1, d-1a-1da, b2, c-1b-1cbd-1, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 8
v b r k Found Comments Where
16 48 15 5 4 here
16 48 15 5 Near-Resolved
16 80 15 3 26 here
16 80 15 3 Near-Resolved

Group 9: non-abelian, with relators: {a2d-1, b-1a-1bac-1, c-1a-1cad-1, d-1a-1da, b2d-1, c-1b-1cbd-1, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 9
v b r k Found Comments Where
16 48 15 5 37 here
16 48 15 5 Near-Resolved
16 80 15 3 24+ Stopped here
16 80 15 3 Near-Resolved

Group 10: abelian, with relators: {a2d-1, b-1a-1ba, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1bd, c2, d-1c-1dc, d2 }

BIBDs with v=16 for group 10
v b r k Found Comments Where
16 48 15 5 106 here
16 48 15 5 Near-Resolved
16 80 15 3 6 here
16 80 15 3 Near-Resolved

Group 11: non-abelian, with relators: {a2, b-1a-1bad-1, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2, d-1c-1dc, d2}

BIBDs with v=16 for group 11
v b r k Found Comments Where
16 48 15 5 6 here
16 48 15 5 Near-Resolved
16 80 15 3 5 here
16 80 15 3 Near-Resolved

Group 12: non-abelian, with relators: {a2d-1, b-1a-1bad-1, c-1a-1ca, d-1a-1da, b2d-1, c-1b-1cb, d-1b-1db, c2, d-1c-1dc, d2}

BIBDs with v=16 for group 12
v b r k Found Comments Where
16 48 15 5 31 here
16 48 15 5 Near-Resolved
16 80 15 3 13+ Stopped here
16 80 15 3 Near-Resolved

Group 13: non-abelian, with relators: {a2, b-1a-1bad-1, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2d-1, d-1c-1dc, d2}

BIBDs with v=16 for group 13
v b r k Found Comments Where
16 48 15 5 21 here
16 48 15 5 Near-Resolved
16 80 15 3 11+ Stopped here
16 80 15 3 Near-Resolved

Group 14: abelian, with relators: {a2,b-1a-1ba, c-1a-1ca, d-1a-1da, b2, c-1b-1cb, d-1b-1db, c2, d-1c-1dc, d2}.

BIBDs with v=16 for group 14
v b r k Found Comments Where
16 48 15 5 1 here
16 48 15 5 Near-Resolved
16 80 15 3 1 here
16 80 15 3 Near-Resolved

Last Updated on 14/10/2004
By D.H.Rees