Best Known (66, 66+48, s)-Nets in Base 16
(66, 66+48, 532)-Net over F16 — Constructive and digital
Digital (66, 114, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 57, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(66, 66+48, 1052)-Net over F16 — Digital
Digital (66, 114, 1052)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16114, 1052, F16, 48) (dual of [1052, 938, 49]-code), using
- 24 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 21 times 0) [i] based on linear OA(16112, 1026, F16, 48) (dual of [1026, 914, 49]-code), using
- trace code [i] based on linear OA(25656, 513, F256, 48) (dual of [513, 457, 49]-code), using
- extended algebraic-geometric code AGe(F,464P) [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,464P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25656, 513, F256, 48) (dual of [513, 457, 49]-code), using
- 24 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 21 times 0) [i] based on linear OA(16112, 1026, F16, 48) (dual of [1026, 914, 49]-code), using
(66, 66+48, 342629)-Net in Base 16 — Upper bound on s
There is no (66, 114, 342630)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 186076 838145 232762 909024 649880 870736 421309 660944 119820 714497 269501 229629 357235 330466 304522 319375 200950 780178 271165 586539 915448 603040 247676 > 16114 [i]