Best Known (85−36, 85, s)-Nets in Base 16
(85−36, 85, 526)-Net over F16 — Constructive and digital
Digital (49, 85, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (49, 86, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 43, 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, 43, 263)-net over F256, using
(85−36, 85, 797)-Net over F16 — Digital
Digital (49, 85, 797)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1685, 797, F16, 36) (dual of [797, 712, 37]-code), using
- 208 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 27 times 0, 1, 40 times 0, 1, 50 times 0, 1, 57 times 0) [i] based on linear OA(1674, 578, F16, 36) (dual of [578, 504, 37]-code), using
- trace code [i] based on linear OA(25637, 289, F256, 36) (dual of [289, 252, 37]-code), using
- extended algebraic-geometric code AGe(F,252P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- trace code [i] based on linear OA(25637, 289, F256, 36) (dual of [289, 252, 37]-code), using
- 208 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 27 times 0, 1, 40 times 0, 1, 50 times 0, 1, 57 times 0) [i] based on linear OA(1674, 578, F16, 36) (dual of [578, 504, 37]-code), using
(85−36, 85, 244423)-Net in Base 16 — Upper bound on s
There is no (49, 85, 244424)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 239758 074854 026749 284368 307702 421299 915944 921935 627634 276528 489397 742506 213697 963427 474318 664520 246356 > 1685 [i]