Best Known (36, 51, s)-Nets in Base 64
(36, 51, 37529)-Net over F64 — Constructive and digital
Digital (36, 51, 37529)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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 (28, 43, 37449)-net over F64, using
- net defined by OOA [i] based on linear OOA(6443, 37449, F64, 15, 15) (dual of [(37449, 15), 561692, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using
- net defined by OOA [i] based on linear OOA(6443, 37449, F64, 15, 15) (dual of [(37449, 15), 561692, 16]-NRT-code), using
- digital (1, 8, 80)-net over F64, using
(36, 51, 299593)-Net in Base 64 — Constructive
(36, 51, 299593)-net in base 64, using
- net defined by OOA [i] based on OOA(6451, 299593, S64, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(6451, 2097152, S64, 15), using
- discarding factors based on OA(6451, 2097155, S64, 15), using
- discarding parts of the base [i] based on linear OA(12843, 2097155, F128, 15) (dual of [2097155, 2097112, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(12843, 2097155, F128, 15) (dual of [2097155, 2097112, 16]-code), using
- discarding factors based on OA(6451, 2097155, S64, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(6451, 2097152, S64, 15), using
(36, 51, 364570)-Net over F64 — Digital
Digital (36, 51, 364570)-net over F64, using
(36, 51, large)-Net in Base 64 — Upper bound on s
There is no (36, 51, large)-net in base 64, because
- 13 times m-reduction [i] would yield (36, 38, large)-net in base 64, but