Best Known (50−20, 50, s)-Nets in Base 16
(50−20, 50, 531)-Net over F16 — Constructive and digital
Digital (30, 50, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (20, 40, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 20, 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, 20, 257)-net over F256, using
- digital (0, 10, 17)-net over F16, using
(50−20, 50, 795)-Net over F16 — Digital
Digital (30, 50, 795)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1650, 795, F16, 20) (dual of [795, 745, 21]-code), using
- 147 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 14 times 0, 1, 42 times 0, 1, 84 times 0) [i] based on linear OA(1644, 642, F16, 20) (dual of [642, 598, 21]-code), using
- trace code [i] based on linear OA(25622, 321, F256, 20) (dual of [321, 299, 21]-code), using
- extended algebraic-geometric code AGe(F,300P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25622, 321, F256, 20) (dual of [321, 299, 21]-code), using
- 147 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 14 times 0, 1, 42 times 0, 1, 84 times 0) [i] based on linear OA(1644, 642, F16, 20) (dual of [642, 598, 21]-code), using
(50−20, 50, 316575)-Net in Base 16 — Upper bound on s
There is no (30, 50, 316576)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 606942 398660 718185 953702 757813 870125 226682 706118 404214 510901 > 1650 [i]