Best Known (73−26, 73, s)-Nets in Base 64
(73−26, 73, 665)-Net over F64 — Constructive and digital
Digital (47, 73, 665)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- digital (0, 2, 65)-net over F64 (see above)
- 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, 3, 65)-net over F64 (see above)
- digital (0, 4, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 13, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (1, 27, 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
(73−26, 73, 5042)-Net in Base 64 — Constructive
(47, 73, 5042)-net in base 64, using
- 641 times duplication [i] based on (46, 72, 5042)-net in base 64, using
- base change [i] based on digital (28, 54, 5042)-net over F256, using
- net defined by OOA [i] based on linear OOA(25654, 5042, F256, 26, 26) (dual of [(5042, 26), 131038, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25654, 65546, F256, 26) (dual of [65546, 65492, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25654, 65546, F256, 26) (dual of [65546, 65492, 27]-code), using
- net defined by OOA [i] based on linear OOA(25654, 5042, F256, 26, 26) (dual of [(5042, 26), 131038, 27]-NRT-code), using
- base change [i] based on digital (28, 54, 5042)-net over F256, using
(73−26, 73, 30375)-Net over F64 — Digital
Digital (47, 73, 30375)-net over F64, using
(73−26, 73, large)-Net in Base 64 — Upper bound on s
There is no (47, 73, large)-net in base 64, because
- 24 times m-reduction [i] would yield (47, 49, large)-net in base 64, but