Best Known (34, 34+14, s)-Nets in Base 64
(34, 34+14, 37529)-Net over F64 — Constructive and digital
Digital (34, 48, 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 (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 (1, 8, 80)-net over F64, using
(34, 34+14, 299594)-Net in Base 64 — Constructive
(34, 48, 299594)-net in base 64, using
- net defined by OOA [i] based on OOA(6448, 299594, S64, 14, 14), using
- OA 7-folding and stacking [i] based on OA(6448, 2097158, S64, 14), using
- discarding factors based on OA(6448, 2097159, S64, 14), using
- discarding parts of the base [i] based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [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(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(13) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-code), using
- discarding factors based on OA(6448, 2097159, S64, 14), using
- OA 7-folding and stacking [i] based on OA(6448, 2097158, S64, 14), using
(34, 34+14, 419802)-Net over F64 — Digital
Digital (34, 48, 419802)-net over F64, using
(34, 34+14, large)-Net in Base 64 — Upper bound on s
There is no (34, 48, large)-net in base 64, because
- 12 times m-reduction [i] would yield (34, 36, large)-net in base 64, but