Best Known (23, 23+15, s)-Nets in Base 16
(23, 23+15, 538)-Net over F16 — Constructive and digital
Digital (23, 38, 538)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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 (15, 30, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 15, 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, 15, 257)-net over F256, using
- digital (1, 8, 24)-net over F16, using
(23, 23+15, 772)-Net over F16 — Digital
Digital (23, 38, 772)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1638, 772, F16, 15) (dual of [772, 734, 16]-code), using
- 126 step Varšamov–Edel lengthening with (ri) = (2, 7 times 0, 1, 31 times 0, 1, 85 times 0) [i] based on linear OA(1634, 642, F16, 15) (dual of [642, 608, 16]-code), using
- trace code [i] based on linear OA(25617, 321, F256, 15) (dual of [321, 304, 16]-code), using
- extended algebraic-geometric code AGe(F,305P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25617, 321, F256, 15) (dual of [321, 304, 16]-code), using
- 126 step Varšamov–Edel lengthening with (ri) = (2, 7 times 0, 1, 31 times 0, 1, 85 times 0) [i] based on linear OA(1634, 642, F16, 15) (dual of [642, 608, 16]-code), using
(23, 23+15, 521745)-Net in Base 16 — Upper bound on s
There is no (23, 38, 521746)-net in base 16, because
- 1 times m-reduction [i] would yield (23, 37, 521746)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 356 814400 478288 626052 339354 436448 659941 186056 > 1637 [i]