Best Known (66−27, 66, s)-Nets in Base 16
(66−27, 66, 526)-Net over F16 — Constructive and digital
Digital (39, 66, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 33, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(66−27, 66, 816)-Net over F16 — Digital
Digital (39, 66, 816)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1666, 816, F16, 27) (dual of [816, 750, 28]-code), using
- 166 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 11 times 0, 1, 25 times 0, 1, 49 times 0, 1, 71 times 0) [i] based on linear OA(1658, 642, F16, 27) (dual of [642, 584, 28]-code), using
- trace code [i] based on linear OA(25629, 321, F256, 27) (dual of [321, 292, 28]-code), using
- extended algebraic-geometric code AGe(F,293P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25629, 321, F256, 27) (dual of [321, 292, 28]-code), using
- 166 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 11 times 0, 1, 25 times 0, 1, 49 times 0, 1, 71 times 0) [i] based on linear OA(1658, 642, F16, 27) (dual of [642, 584, 28]-code), using
(66−27, 66, 396193)-Net in Base 16 — Upper bound on s
There is no (39, 66, 396194)-net in base 16, because
- 1 times m-reduction [i] would yield (39, 65, 396194)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 852706 078807 265750 635240 673256 087404 725153 944239 619066 277317 536753 771841 270456 > 1665 [i]