Best Known (22, 32, s)-Nets in Base 8
(22, 32, 290)-Net over F8 — Constructive and digital
Digital (22, 32, 290)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 130)-net over F8, using
- trace code for nets [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
- trace code for nets [i] based on digital (0, 5, 65)-net over F64, using
- digital (12, 22, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 11, 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
- trace code for nets [i] based on digital (1, 11, 80)-net over F64, using
- digital (5, 10, 130)-net over F8, using
(22, 32, 518)-Net in Base 8 — Constructive
(22, 32, 518)-net in base 8, using
- base change [i] based on digital (14, 24, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 12, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 12, 259)-net over F256, using
(22, 32, 971)-Net over F8 — Digital
Digital (22, 32, 971)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(832, 971, F8, 10) (dual of [971, 939, 11]-code), using
- 449 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 34 times 0, 1, 75 times 0, 1, 131 times 0, 1, 188 times 0) [i] based on linear OA(825, 515, F8, 10) (dual of [515, 490, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(825, 512, F8, 10) (dual of [512, 487, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 449 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 34 times 0, 1, 75 times 0, 1, 131 times 0, 1, 188 times 0) [i] based on linear OA(825, 515, F8, 10) (dual of [515, 490, 11]-code), using
(22, 32, 224134)-Net in Base 8 — Upper bound on s
There is no (22, 32, 224135)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 79228 903911 706696 451144 287490 > 832 [i]