Best Known (33, 33+14, s)-Nets in Base 64
(33, 33+14, 37514)-Net over F64 — Constructive and digital
Digital (33, 47, 37514)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (26, 40, 37449)-net over F64, using
- net defined by OOA [i] based on linear OOA(6440, 37449, F64, 14, 14) (dual of [(37449, 14), 524246, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6440, 262143, F64, 14) (dual of [262143, 262103, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6440, 262143, F64, 14) (dual of [262143, 262103, 15]-code), using
- net defined by OOA [i] based on linear OOA(6440, 37449, F64, 14, 14) (dual of [(37449, 14), 524246, 15]-NRT-code), using
- digital (0, 7, 65)-net over F64, using
(33, 33+14, 299593)-Net in Base 64 — Constructive
(33, 47, 299593)-net in base 64, using
- net defined by OOA [i] based on OOA(6447, 299593, S64, 14, 14), using
- OA 7-folding and stacking [i] based on OA(6447, 2097151, S64, 14), using
- discarding factors based on OA(6447, 2097155, S64, 14), using
- discarding parts of the base [i] based on linear OA(12840, 2097155, F128, 14) (dual of [2097155, 2097115, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(12840, 2097155, F128, 14) (dual of [2097155, 2097115, 15]-code), using
- discarding factors based on OA(6447, 2097155, S64, 14), using
- OA 7-folding and stacking [i] based on OA(6447, 2097151, S64, 14), using
(33, 33+14, 304867)-Net over F64 — Digital
Digital (33, 47, 304867)-net over F64, using
(33, 33+14, large)-Net in Base 64 — Upper bound on s
There is no (33, 47, large)-net in base 64, because
- 12 times m-reduction [i] would yield (33, 35, large)-net in base 64, but