Best Known (8, 18, s)-Nets in Base 64
(8, 18, 195)-Net over F64 — Constructive and digital
Digital (8, 18, 195)-net over F64, using
- 1 times m-reduction [i] based on digital (8, 19, 195)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 11, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 3, 65)-net over F64, using
- generalized (u, u+v)-construction [i] based on
(8, 18, 260)-Net in Base 64 — Constructive
(8, 18, 260)-net in base 64, using
- 2 times m-reduction [i] based on (8, 20, 260)-net in base 64, using
- base change [i] based on digital (3, 15, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 15, 260)-net over F256, using
(8, 18, 409)-Net over F64 — Digital
Digital (8, 18, 409)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6418, 409, F64, 10) (dual of [409, 391, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6418, 585, F64, 10) (dual of [585, 567, 11]-code), using
(8, 18, 131442)-Net in Base 64 — Upper bound on s
There is no (8, 18, 131443)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 324 521269 273876 711157 527708 028728 > 6418 [i]