Best Known (86−25, 86, s)-Nets in Base 64
(86−25, 86, 21925)-Net over F64 — Constructive and digital
Digital (61, 86, 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 (48, 73, 21845)-net over F64, using
- net defined by OOA [i] based on linear OOA(6473, 21845, F64, 25, 25) (dual of [(21845, 25), 546052, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6473, 262141, F64, 25) (dual of [262141, 262068, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6473, 262141, F64, 25) (dual of [262141, 262068, 26]-code), using
- net defined by OOA [i] based on linear OOA(6473, 21845, F64, 25, 25) (dual of [(21845, 25), 546052, 26]-NRT-code), using
- digital (1, 13, 80)-net over F64, using
(86−25, 86, 174762)-Net in Base 64 — Constructive
(61, 86, 174762)-net in base 64, using
- net defined by OOA [i] based on OOA(6486, 174762, S64, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6486, 2097145, S64, 25), using
- discarding factors based on OA(6486, 2097155, S64, 25), using
- discarding parts of the base [i] based on linear OA(12873, 2097155, F128, 25) (dual of [2097155, 2097082, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(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(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(12873, 2097155, F128, 25) (dual of [2097155, 2097082, 26]-code), using
- discarding factors based on OA(6486, 2097155, S64, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6486, 2097145, S64, 25), using
(86−25, 86, 461507)-Net over F64 — Digital
Digital (61, 86, 461507)-net over F64, using
(86−25, 86, large)-Net in Base 64 — Upper bound on s
There is no (61, 86, large)-net in base 64, because
- 23 times m-reduction [i] would yield (61, 63, large)-net in base 64, but