Best Known (68−28, 68, s)-Nets in Base 16
(68−28, 68, 526)-Net over F16 — Constructive and digital
Digital (40, 68, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 34, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(68−28, 68, 801)-Net over F16 — Digital
Digital (40, 68, 801)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1668, 801, F16, 28) (dual of [801, 733, 29]-code), using
- 151 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 0, 1, 9 times 0, 1, 23 times 0, 1, 44 times 0, 1, 66 times 0) [i] based on linear OA(1660, 642, F16, 28) (dual of [642, 582, 29]-code), using
- trace code [i] based on linear OA(25630, 321, F256, 28) (dual of [321, 291, 29]-code), using
- extended algebraic-geometric code AGe(F,292P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25630, 321, F256, 28) (dual of [321, 291, 29]-code), using
- 151 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 0, 1, 9 times 0, 1, 23 times 0, 1, 44 times 0, 1, 66 times 0) [i] based on linear OA(1660, 642, F16, 28) (dual of [642, 582, 29]-code), using
(68−28, 68, 284405)-Net in Base 16 — Upper bound on s
There is no (40, 68, 284406)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7588 758700 699847 348546 187605 663095 055391 676701 400795 907757 375832 547358 946676 133736 > 1668 [i]