Best Known (65, 91, s)-Nets in Base 8
(65, 91, 419)-Net over F8 — Constructive and digital
Digital (65, 91, 419)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (12, 25, 65)-net over F8, using
- base reduction for projective spaces (embedding PG(12,64) in PG(24,8)) for nets [i] based on digital (0, 13, 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
- base reduction for projective spaces (embedding PG(12,64) in PG(24,8)) for nets [i] based on digital (0, 13, 65)-net over F64, using
- digital (40, 66, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 33, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 33, 177)-net over F64, using
- digital (12, 25, 65)-net over F8, using
(65, 91, 576)-Net in Base 8 — Constructive
(65, 91, 576)-net in base 8, using
- 7 times m-reduction [i] based on (65, 98, 576)-net in base 8, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
(65, 91, 3397)-Net over F8 — Digital
Digital (65, 91, 3397)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(891, 3397, F8, 26) (dual of [3397, 3306, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 4105, F8, 26) (dual of [4105, 4014, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(889, 4096, F8, 26) (dual of [4096, 4007, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(881, 4096, F8, 23) (dual of [4096, 4015, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(891, 4105, F8, 26) (dual of [4105, 4014, 27]-code), using
(65, 91, 1697993)-Net in Base 8 — Upper bound on s
There is no (65, 91, 1697994)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 15177 152415 880119 714807 438609 318155 164390 867711 427324 174017 586347 092505 924271 512080 > 891 [i]