Best Known (56, 56+34, s)-Nets in Base 64
(56, 56+34, 690)-Net over F64 — Constructive and digital
Digital (56, 90, 690)-net over F64, using
- t-expansion [i] based on digital (53, 90, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 65, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- digital (7, 25, 177)-net over F64, using
- (u, u+v)-construction [i] based on
(56, 56+34, 3855)-Net in Base 64 — Constructive
(56, 90, 3855)-net in base 64, using
- net defined by OOA [i] based on OOA(6490, 3855, S64, 34, 34), using
- OA 17-folding and stacking [i] based on OA(6490, 65535, S64, 34), using
- discarding factors based on OA(6490, 65538, S64, 34), using
- discarding parts of the base [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(25667, 65536, F256, 34) (dual of [65536, 65469, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(25665, 65536, F256, 33) (dual of [65536, 65471, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(33) ⊂ Ce(32) [i] based on
- discarding parts of the base [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
- discarding factors based on OA(6490, 65538, S64, 34), using
- OA 17-folding and stacking [i] based on OA(6490, 65535, S64, 34), using
(56, 56+34, 17635)-Net over F64 — Digital
Digital (56, 90, 17635)-net over F64, using
(56, 56+34, large)-Net in Base 64 — Upper bound on s
There is no (56, 90, large)-net in base 64, because
- 32 times m-reduction [i] would yield (56, 58, large)-net in base 64, but