Best Known (57, 80, s)-Nets in Base 64
(57, 80, 23911)-Net over F64 — Constructive and digital
Digital (57, 80, 23911)-net over F64, using
- 641 times duplication [i] based on digital (56, 79, 23911)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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
- digital (44, 67, 23831)-net over F64, using
- net defined by OOA [i] based on linear OOA(6467, 23831, F64, 23, 23) (dual of [(23831, 23), 548046, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6467, 262142, F64, 23) (dual of [262142, 262075, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6467, 262142, F64, 23) (dual of [262142, 262075, 24]-code), using
- net defined by OOA [i] based on linear OOA(6467, 23831, F64, 23, 23) (dual of [(23831, 23), 548046, 24]-NRT-code), using
- digital (1, 12, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(57, 80, 190650)-Net in Base 64 — Constructive
(57, 80, 190650)-net in base 64, using
- 641 times duplication [i] based on (56, 79, 190650)-net in base 64, using
- net defined by OOA [i] based on OOA(6479, 190650, S64, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6479, 2097151, S64, 23), using
- discarding factors based on OA(6479, 2097155, S64, 23), using
- discarding parts of the base [i] based on linear OA(12867, 2097155, F128, 23) (dual of [2097155, 2097088, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(12867, 2097155, F128, 23) (dual of [2097155, 2097088, 24]-code), using
- discarding factors based on OA(6479, 2097155, S64, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6479, 2097151, S64, 23), using
- net defined by OOA [i] based on OOA(6479, 190650, S64, 23, 23), using
(57, 80, 531433)-Net over F64 — Digital
Digital (57, 80, 531433)-net over F64, using
(57, 80, large)-Net in Base 64 — Upper bound on s
There is no (57, 80, large)-net in base 64, because
- 21 times m-reduction [i] would yield (57, 59, large)-net in base 64, but