Best Known (85−30, 85, s)-Nets in Base 64
(85−30, 85, 708)-Net over F64 — Constructive and digital
Digital (55, 85, 708)-net over F64, using
- 1 times m-reduction [i] based on digital (55, 86, 708)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (12, 27, 195)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 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, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 15, 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
- generalized (u, u+v)-construction [i] based on
- digital (28, 59, 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 (12, 27, 195)-net over F64, using
- (u, u+v)-construction [i] based on
(85−30, 85, 4370)-Net in Base 64 — Constructive
(55, 85, 4370)-net in base 64, using
- 641 times duplication [i] based on (54, 84, 4370)-net in base 64, using
- base change [i] based on digital (33, 63, 4370)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
- base change [i] based on digital (33, 63, 4370)-net over F256, using
(85−30, 85, 36469)-Net over F64 — Digital
Digital (55, 85, 36469)-net over F64, using
(85−30, 85, large)-Net in Base 64 — Upper bound on s
There is no (55, 85, large)-net in base 64, because
- 28 times m-reduction [i] would yield (55, 57, large)-net in base 64, but