Best Known (50, 71, s)-Nets in Base 64
(50, 71, 26279)-Net over F64 — Constructive and digital
Digital (50, 71, 26279)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (40, 61, 26214)-net over F64, using
- net defined by OOA [i] based on linear OOA(6461, 26214, F64, 21, 21) (dual of [(26214, 21), 550433, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(6461, 262141, F64, 21) (dual of [262141, 262080, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(6461, 262141, F64, 21) (dual of [262141, 262080, 22]-code), using
- net defined by OOA [i] based on linear OOA(6461, 26214, F64, 21, 21) (dual of [(26214, 21), 550433, 22]-NRT-code), using
- digital (0, 10, 65)-net over F64, using
(50, 71, 340343)-Net over F64 — Digital
Digital (50, 71, 340343)-net over F64, using
(50, 71, large)-Net in Base 64 — Upper bound on s
There is no (50, 71, large)-net in base 64, because
- 19 times m-reduction [i] would yield (50, 52, large)-net in base 64, but