Best Known (59, 100, s)-Nets in Base 16
(59, 100, 532)-Net over F16 — Constructive and digital
Digital (59, 100, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 50, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(59, 100, 1098)-Net over F16 — Digital
Digital (59, 100, 1098)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16100, 1098, F16, 41) (dual of [1098, 998, 42]-code), using
- 70 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0, 1, 54 times 0) [i] based on linear OA(1698, 1026, F16, 41) (dual of [1026, 928, 42]-code), using
- trace code [i] based on linear OA(25649, 513, F256, 41) (dual of [513, 464, 42]-code), using
- extended algebraic-geometric code AGe(F,471P) [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,471P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25649, 513, F256, 41) (dual of [513, 464, 42]-code), using
- 70 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0, 1, 54 times 0) [i] based on linear OA(1698, 1026, F16, 41) (dual of [1026, 928, 42]-code), using
(59, 100, 505358)-Net in Base 16 — Upper bound on s
There is no (59, 100, 505359)-net in base 16, because
- 1 times m-reduction [i] would yield (59, 99, 505359)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 161393 801064 447935 573518 725281 691826 447935 512910 010451 710560 061372 074694 963913 348204 382810 103146 639417 536803 799036 884576 > 1699 [i]