Best Known (54−22, 54, s)-Nets in Base 64
(54−22, 54, 513)-Net over F64 — Constructive and digital
Digital (32, 54, 513)-net over F64, using
- t-expansion [i] based on digital (28, 54, 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
(54−22, 54, 1490)-Net in Base 64 — Constructive
(32, 54, 1490)-net in base 64, using
- 1 times m-reduction [i] based on (32, 55, 1490)-net in base 64, using
- net defined by OOA [i] based on OOA(6455, 1490, S64, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6455, 16391, S64, 23), using
- discarding factors based on OA(6455, 16392, S64, 23), using
- discarding parts of the base [i] based on linear OA(12847, 16392, F128, 23) (dual of [16392, 16345, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12847, 16392, F128, 23) (dual of [16392, 16345, 24]-code), using
- discarding factors based on OA(6455, 16392, S64, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6455, 16391, S64, 23), using
- net defined by OOA [i] based on OOA(6455, 1490, S64, 23, 23), using
(54−22, 54, 6086)-Net over F64 — Digital
Digital (32, 54, 6086)-net over F64, using
(54−22, 54, large)-Net in Base 64 — Upper bound on s
There is no (32, 54, large)-net in base 64, because
- 20 times m-reduction [i] would yield (32, 34, large)-net in base 64, but