Best Known (16, 16+18, s)-Nets in Base 64
(16, 16+18, 242)-Net over F64 — Constructive and digital
Digital (16, 34, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (0, 9, 65)-net over F64, using
(16, 16+18, 337)-Net in Base 64 — Constructive
(16, 34, 337)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- (6, 24, 257)-net in base 64, using
- base change [i] based on digital (0, 18, 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
- base change [i] based on digital (0, 18, 257)-net over F256, using
- digital (1, 10, 80)-net over F64, using
(16, 16+18, 567)-Net over F64 — Digital
Digital (16, 34, 567)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6434, 567, F64, 18) (dual of [567, 533, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6434, 819, F64, 18) (dual of [819, 785, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 819 | 642−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(6434, 819, F64, 18) (dual of [819, 785, 19]-code), using
(16, 16+18, 438281)-Net in Base 64 — Upper bound on s
There is no (16, 34, 438282)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 25 711154 111329 776940 448184 830282 753246 662038 693641 159793 017983 > 6434 [i]