Best Known (44, 44+27, s)-Nets in Base 64
(44, 44+27, 617)-Net over F64 — Constructive and digital
Digital (44, 71, 617)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 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 (28, 55, 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 (3, 16, 104)-net over F64, using
(44, 44+27, 5041)-Net in Base 64 — Constructive
(44, 71, 5041)-net in base 64, using
- net defined by OOA [i] based on OOA(6471, 5041, S64, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(6471, 65534, S64, 27), using
- discarding factors based on OA(6471, 65538, S64, 27), using
- discarding parts of the base [i] based on linear OA(25653, 65538, F256, 27) (dual of [65538, 65485, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(25653, 65538, F256, 27) (dual of [65538, 65485, 28]-code), using
- discarding factors based on OA(6471, 65538, S64, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(6471, 65534, S64, 27), using
(44, 44+27, 14342)-Net over F64 — Digital
Digital (44, 71, 14342)-net over F64, using
(44, 44+27, large)-Net in Base 64 — Upper bound on s
There is no (44, 71, large)-net in base 64, because
- 25 times m-reduction [i] would yield (44, 46, large)-net in base 64, but