Best Known (23, 23+14, s)-Nets in Base 64
(23, 23+14, 715)-Net over F64 — Constructive and digital
Digital (23, 37, 715)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 130)-net over F64, using
- (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, 7, 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
- (u, u+v)-construction [i] based on
- digital (13, 27, 585)-net over F64, using
- net defined by OOA [i] based on linear OOA(6427, 585, F64, 14, 14) (dual of [(585, 14), 8163, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6427, 4095, F64, 14) (dual of [4095, 4068, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6427, 4095, F64, 14) (dual of [4095, 4068, 15]-code), using
- net defined by OOA [i] based on linear OOA(6427, 585, F64, 14, 14) (dual of [(585, 14), 8163, 15]-NRT-code), using
- digital (3, 10, 130)-net over F64, using
(23, 23+14, 9362)-Net in Base 64 — Constructive
(23, 37, 9362)-net in base 64, using
- 641 times duplication [i] based on (22, 36, 9362)-net in base 64, using
- base change [i] based on digital (13, 27, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25627, 9362, F256, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
- net defined by OOA [i] based on linear OOA(25627, 9362, F256, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
- base change [i] based on digital (13, 27, 9362)-net over F256, using
(23, 23+14, 12444)-Net over F64 — Digital
Digital (23, 37, 12444)-net over F64, using
(23, 23+14, 16384)-Net in Base 64
(23, 37, 16384)-net in base 64, using
- 641 times duplication [i] based on (22, 36, 16384)-net in base 64, using
- base change [i] based on digital (13, 27, 16384)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25627, 16384, F256, 4, 14) (dual of [(16384, 4), 65509, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OOA 4-folding [i] based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25627, 16384, F256, 4, 14) (dual of [(16384, 4), 65509, 15]-NRT-code), using
- base change [i] based on digital (13, 27, 16384)-net over F256, using
(23, 23+14, large)-Net in Base 64 — Upper bound on s
There is no (23, 37, large)-net in base 64, because
- 12 times m-reduction [i] would yield (23, 25, large)-net in base 64, but