Best Known (57, 96, s)-Nets in Base 16
(57, 96, 532)-Net over F16 — Constructive and digital
Digital (57, 96, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 48, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(57, 96, 1123)-Net over F16 — Digital
Digital (57, 96, 1123)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1696, 1123, F16, 39) (dual of [1123, 1027, 40]-code), using
- 95 step Varšamov–Edel lengthening with (ri) = (1, 27 times 0, 1, 66 times 0) [i] based on linear OA(1694, 1026, F16, 39) (dual of [1026, 932, 40]-code), using
- trace code [i] based on linear OA(25647, 513, F256, 39) (dual of [513, 466, 40]-code), using
- extended algebraic-geometric code AGe(F,473P) [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,473P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25647, 513, F256, 39) (dual of [513, 466, 40]-code), using
- 95 step Varšamov–Edel lengthening with (ri) = (1, 27 times 0, 1, 66 times 0) [i] based on linear OA(1694, 1026, F16, 39) (dual of [1026, 932, 40]-code), using
(57, 96, 554263)-Net in Base 16 — Upper bound on s
There is no (57, 96, 554264)-net in base 16, because
- 1 times m-reduction [i] would yield (57, 95, 554264)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 462685 225050 092185 245698 354608 364077 224419 527942 123681 562539 169062 641032 636637 621575 826672 608204 360664 999640 993241 > 1695 [i]