Best Known (70−25, 70, s)-Nets in Base 64
(70−25, 70, 650)-Net over F64 — Constructive and digital
Digital (45, 70, 650)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- digital (0, 2, 65)-net over F64 (see above)
- digital (0, 3, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (0, 3, 65)-net over F64 (see above)
- digital (0, 4, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 12, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 25, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
(70−25, 70, 5462)-Net in Base 64 — Constructive
(45, 70, 5462)-net in base 64, using
- 641 times duplication [i] based on (44, 69, 5462)-net in base 64, using
- net defined by OOA [i] based on OOA(6469, 5462, S64, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6469, 65545, S64, 25), using
- 1 times code embedding in larger space [i] based on OA(6468, 65544, S64, 25), using
- discarding parts of the base [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(24) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- 1 times code embedding in larger space [i] based on OA(6468, 65544, S64, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6469, 65545, S64, 25), using
- net defined by OOA [i] based on OOA(6469, 5462, S64, 25, 25), using
(70−25, 70, 28855)-Net over F64 — Digital
Digital (45, 70, 28855)-net over F64, using
(70−25, 70, large)-Net in Base 64 — Upper bound on s
There is no (45, 70, large)-net in base 64, because
- 23 times m-reduction [i] would yield (45, 47, large)-net in base 64, but