Best Known (21, 21+14, s)-Nets in Base 16
(21, 21+14, 531)-Net over F16 — Constructive and digital
Digital (21, 35, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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, 14, 257)-net over F256, using
- digital (0, 7, 17)-net over F16, using
(21, 21+14, 708)-Net over F16 — Digital
Digital (21, 35, 708)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1635, 708, F16, 14) (dual of [708, 673, 15]-code), using
- 63 step Varšamov–Edel lengthening with (ri) = (2, 10 times 0, 1, 51 times 0) [i] based on linear OA(1632, 642, F16, 14) (dual of [642, 610, 15]-code), using
- trace code [i] based on linear OA(25616, 321, F256, 14) (dual of [321, 305, 15]-code), using
- extended algebraic-geometric code AGe(F,306P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25616, 321, F256, 14) (dual of [321, 305, 15]-code), using
- 63 step Varšamov–Edel lengthening with (ri) = (2, 10 times 0, 1, 51 times 0) [i] based on linear OA(1632, 642, F16, 14) (dual of [642, 610, 15]-code), using
(21, 21+14, 236276)-Net in Base 16 — Upper bound on s
There is no (21, 35, 236277)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 393808 203623 308045 244239 179708 748145 405136 > 1635 [i]