Best Known (39, 63, s)-Nets in Base 64
(39, 63, 513)-Net over F64 — Constructive and digital
Digital (39, 63, 513)-net over F64, using
- t-expansion [i] based on digital (28, 63, 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
(39, 63, 5461)-Net in Base 64 — Constructive
(39, 63, 5461)-net in base 64, using
- net defined by OOA [i] based on OOA(6463, 5461, S64, 24, 24), using
- OA 12-folding and stacking [i] based on OA(6463, 65532, S64, 24), using
- discarding factors based on OA(6463, 65538, S64, 24), using
- discarding parts of the base [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- discarding factors based on OA(6463, 65538, S64, 24), using
- OA 12-folding and stacking [i] based on OA(6463, 65532, S64, 24), using
(39, 63, 13269)-Net over F64 — Digital
Digital (39, 63, 13269)-net over F64, using
(39, 63, large)-Net in Base 64 — Upper bound on s
There is no (39, 63, large)-net in base 64, because
- 22 times m-reduction [i] would yield (39, 41, large)-net in base 64, but