Best Known (98−40, 98, s)-Nets in Base 16
(98−40, 98, 532)-Net over F16 — Constructive and digital
Digital (58, 98, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 49, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(98−40, 98, 1110)-Net over F16 — Digital
Digital (58, 98, 1110)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1698, 1110, F16, 40) (dual of [1110, 1012, 41]-code), using
- 82 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0, 1, 60 times 0) [i] based on linear OA(1696, 1026, F16, 40) (dual of [1026, 930, 41]-code), using
- trace code [i] based on linear OA(25648, 513, F256, 40) (dual of [513, 465, 41]-code), using
- extended algebraic-geometric code AGe(F,472P) [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,472P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25648, 513, F256, 40) (dual of [513, 465, 41]-code), using
- 82 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0, 1, 60 times 0) [i] based on linear OA(1696, 1026, F16, 40) (dual of [1026, 930, 41]-code), using
(98−40, 98, 439938)-Net in Base 16 — Upper bound on s
There is no (58, 98, 439939)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 10087 039305 634509 079001 690866 723056 989217 932413 822879 972416 093256 502354 750138 341021 078496 239991 932989 572135 192704 348576 > 1698 [i]