Best Known (91−39, 91, s)-Nets in Base 16
(91−39, 91, 526)-Net over F16 — Constructive and digital
Digital (52, 91, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (52, 92, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 46, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 46, 263)-net over F256, using
(91−39, 91, 786)-Net over F16 — Digital
Digital (52, 91, 786)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1691, 786, F16, 39) (dual of [786, 695, 40]-code), using
- 135 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 38 times 0, 1, 49 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- extended algebraic-geometric code AGe(F,281P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- 135 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 38 times 0, 1, 49 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
(91−39, 91, 267198)-Net in Base 16 — Upper bound on s
There is no (52, 91, 267199)-net in base 16, because
- 1 times m-reduction [i] would yield (52, 90, 267199)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 348648 828294 380926 886273 385627 947295 326843 644808 111047 372557 639540 260931 552027 292199 056394 968066 014217 941716 > 1690 [i]