Best Known (18, 18+12, s)-Nets in Base 16
(18, 18+12, 531)-Net over F16 — Constructive and digital
Digital (18, 30, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- digital (0, 6, 17)-net over F16, using
(18, 18+12, 680)-Net over F16 — Digital
Digital (18, 30, 680)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1630, 680, F16, 12) (dual of [680, 650, 13]-code), using
- 36 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 33 times 0) [i] based on linear OA(1628, 642, F16, 12) (dual of [642, 614, 13]-code), using
- trace code [i] based on linear OA(25614, 321, F256, 12) (dual of [321, 307, 13]-code), using
- extended algebraic-geometric code AGe(F,308P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25614, 321, F256, 12) (dual of [321, 307, 13]-code), using
- 36 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 33 times 0) [i] based on linear OA(1628, 642, F16, 12) (dual of [642, 614, 13]-code), using
(18, 18+12, 209278)-Net in Base 16 — Upper bound on s
There is no (18, 30, 209279)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 329245 120072 906064 012644 684014 975111 > 1630 [i]