Best Known (49, 86, s)-Nets in Base 16
(49, 86, 526)-Net over F16 — Constructive and digital
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
(49, 86, 739)-Net over F16 — Digital
Digital (49, 86, 739)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1686, 739, F16, 37) (dual of [739, 653, 38]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 26 times 0, 1, 40 times 0) [i] based on linear OA(1678, 642, F16, 37) (dual of [642, 564, 38]-code), using
- trace code [i] based on linear OA(25639, 321, F256, 37) (dual of [321, 282, 38]-code), using
- extended algebraic-geometric code AGe(F,283P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25639, 321, F256, 37) (dual of [321, 282, 38]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 26 times 0, 1, 40 times 0) [i] based on linear OA(1678, 642, F16, 37) (dual of [642, 564, 38]-code), using
(49, 86, 244423)-Net in Base 16 — Upper bound on s
There is no (49, 86, 244424)-net in base 16, because
- 1 times m-reduction [i] would yield (49, 85, 244424)-net in base 16, but
- 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]