Best Known (63−25, 63, s)-Nets in Base 16
(63−25, 63, 538)-Net over F16 — Constructive and digital
Digital (38, 63, 538)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (25, 50, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 25, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 25, 257)-net over F256, using
- digital (1, 13, 24)-net over F16, using
(63−25, 63, 959)-Net over F16 — Digital
Digital (38, 63, 959)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1663, 959, F16, 25) (dual of [959, 896, 26]-code), using
- 370 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0, 1, 51 times 0, 1, 73 times 0, 1, 88 times 0, 1, 101 times 0) [i] based on linear OA(1652, 578, F16, 25) (dual of [578, 526, 26]-code), using
- trace code [i] based on linear OA(25626, 289, F256, 25) (dual of [289, 263, 26]-code), using
- extended algebraic-geometric code AGe(F,263P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- trace code [i] based on linear OA(25626, 289, F256, 25) (dual of [289, 263, 26]-code), using
- 370 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0, 1, 51 times 0, 1, 73 times 0, 1, 88 times 0, 1, 101 times 0) [i] based on linear OA(1652, 578, F16, 25) (dual of [578, 526, 26]-code), using
(63−25, 63, 586883)-Net in Base 16 — Upper bound on s
There is no (38, 63, 586884)-net in base 16, because
- 1 times m-reduction [i] would yield (38, 62, 586884)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 452 315347 634791 447421 713492 922733 636260 066872 233702 724255 918023 471080 310496 > 1662 [i]