Best Known (60−14, 60, s)-Nets in Base 64
(60−14, 60, 1198436)-Net over F64 — Constructive and digital
Digital (46, 60, 1198436)-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 (39, 53, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- digital (0, 7, 65)-net over F64, using
(60−14, 60, large)-Net over F64 — Digital
Digital (46, 60, large)-net over F64, using
- 641 times duplication [i] based on digital (45, 59, large)-net over F64, using
- t-expansion [i] based on digital (44, 59, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6459, large, F64, 15) (dual of [large, large−59, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 2 times code embedding in larger space [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6459, large, F64, 15) (dual of [large, large−59, 16]-code), using
- t-expansion [i] based on digital (44, 59, large)-net over F64, using
(60−14, 60, large)-Net in Base 64 — Upper bound on s
There is no (46, 60, large)-net in base 64, because
- 12 times m-reduction [i] would yield (46, 48, large)-net in base 64, but