Best Known (42, 66, s)-Nets in Base 64
(42, 66, 593)-Net over F64 — Constructive and digital
Digital (42, 66, 593)-net over F64, using
- 2 times m-reduction [i] based on digital (42, 68, 593)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- 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
- digital (1, 14, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(42, 66, 5462)-Net in Base 64 — Constructive
(42, 66, 5462)-net in base 64, using
- net defined by OOA [i] based on OOA(6466, 5462, S64, 24, 24), using
- OA 12-folding and stacking [i] based on OA(6466, 65544, S64, 24), using
- discarding parts of the base [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [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(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- OA 12-folding and stacking [i] based on OA(6466, 65544, S64, 24), using
(42, 66, 22818)-Net over F64 — Digital
Digital (42, 66, 22818)-net over F64, using
(42, 66, large)-Net in Base 64 — Upper bound on s
There is no (42, 66, large)-net in base 64, because
- 22 times m-reduction [i] would yield (42, 44, large)-net in base 64, but