Best Known (83−24, 83, s)-Nets in Base 64
(83−24, 83, 21925)-Net over F64 — Constructive and digital
Digital (59, 83, 21925)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (46, 70, 21845)-net over F64, using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- digital (1, 13, 80)-net over F64, using
(83−24, 83, 174763)-Net in Base 64 — Constructive
(59, 83, 174763)-net in base 64, using
- net defined by OOA [i] based on OOA(6483, 174763, S64, 24, 24), using
- OA 12-folding and stacking [i] based on OA(6483, 2097156, S64, 24), using
- discarding factors based on OA(6483, 2097159, S64, 24), using
- discarding parts of the base [i] based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- discarding factors based on OA(6483, 2097159, S64, 24), using
- OA 12-folding and stacking [i] based on OA(6483, 2097156, S64, 24), using
(83−24, 83, 493264)-Net over F64 — Digital
Digital (59, 83, 493264)-net over F64, using
(83−24, 83, large)-Net in Base 64 — Upper bound on s
There is no (59, 83, large)-net in base 64, because
- 22 times m-reduction [i] would yield (59, 61, large)-net in base 64, but