Best Known (92−37, 92, s)-Nets in Base 16
(92−37, 92, 532)-Net over F16 — Constructive and digital
Digital (55, 92, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 46, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(92−37, 92, 1156)-Net over F16 — Digital
Digital (55, 92, 1156)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1692, 1156, F16, 37) (dual of [1156, 1064, 38]-code), using
- 128 step Varšamov–Edel lengthening with (ri) = (1, 47 times 0, 1, 79 times 0) [i] based on linear OA(1690, 1026, F16, 37) (dual of [1026, 936, 38]-code), using
- trace code [i] based on linear OA(25645, 513, F256, 37) (dual of [513, 468, 38]-code), using
- extended algebraic-geometric code AGe(F,475P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,475P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25645, 513, F256, 37) (dual of [513, 468, 38]-code), using
- 128 step Varšamov–Edel lengthening with (ri) = (1, 47 times 0, 1, 79 times 0) [i] based on linear OA(1690, 1026, F16, 37) (dual of [1026, 936, 38]-code), using
(92−37, 92, 615924)-Net in Base 16 — Upper bound on s
There is no (55, 92, 615925)-net in base 16, because
- 1 times m-reduction [i] would yield (55, 91, 615925)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 37 577313 898829 891547 237366 221531 777269 052620 688380 316336 526379 747757 844980 465339 279410 065314 142573 683548 691626 > 1691 [i]