Best Known (18, 39, s)-Nets in Base 256
(18, 39, 772)-Net over F256 — Constructive and digital
Digital (18, 39, 772)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 7, 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
- digital (0, 10, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (1, 22, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (0, 7, 257)-net over F256, using
(18, 39, 1628)-Net over F256 — Digital
Digital (18, 39, 1628)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25639, 1628, F256, 21) (dual of [1628, 1589, 22]-code), using
- 341 step Varšamov–Edel lengthening with (ri) = (1, 22 times 0, 1, 317 times 0) [i] based on linear OA(25637, 1285, F256, 21) (dual of [1285, 1248, 22]-code), using
(18, 39, large)-Net in Base 256 — Upper bound on s
There is no (18, 39, large)-net in base 256, because
- 19 times m-reduction [i] would yield (18, 20, large)-net in base 256, but