Best Known (42−16, 42, s)-Nets in Base 64
(42−16, 42, 616)-Net over F64 — Constructive and digital
Digital (26, 42, 616)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (15, 31, 512)-net over F64, using
- net defined by OOA [i] based on linear OOA(6431, 512, F64, 16, 16) (dual of [(512, 16), 8161, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using
- net defined by OOA [i] based on linear OOA(6431, 512, F64, 16, 16) (dual of [(512, 16), 8161, 17]-NRT-code), using
- digital (3, 11, 104)-net over F64, using
(42−16, 42, 8192)-Net in Base 64 — Constructive
(26, 42, 8192)-net in base 64, using
- net defined by OOA [i] based on OOA(6442, 8192, S64, 16, 16), using
- OA 8-folding and stacking [i] based on OA(6442, 65536, S64, 16), using
- discarding factors based on OA(6442, 65538, S64, 16), using
- discarding parts of the base [i] based on linear OA(25631, 65538, F256, 16) (dual of [65538, 65507, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(25631, 65538, F256, 16) (dual of [65538, 65507, 17]-code), using
- discarding factors based on OA(6442, 65538, S64, 16), using
- OA 8-folding and stacking [i] based on OA(6442, 65536, S64, 16), using
(42−16, 42, 11642)-Net over F64 — Digital
Digital (26, 42, 11642)-net over F64, using
(42−16, 42, large)-Net in Base 64 — Upper bound on s
There is no (26, 42, large)-net in base 64, because
- 14 times m-reduction [i] would yield (26, 28, large)-net in base 64, but