Best Known (30, 30+24, s)-Nets in Base 32
(30, 30+24, 218)-Net over F32 — Constructive and digital
Digital (30, 54, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (11, 35, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (7, 19, 98)-net over F32, using
(30, 30+24, 337)-Net in Base 32 — Constructive
(30, 54, 337)-net in base 32, using
- base change [i] based on (21, 45, 337)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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
- (8, 32, 257)-net in base 64, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
- digital (1, 13, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(30, 30+24, 1131)-Net over F32 — Digital
Digital (30, 54, 1131)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3254, 1131, F32, 24) (dual of [1131, 1077, 25]-code), using
- 97 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 9 times 0, 1, 25 times 0, 1, 57 times 0) [i] based on linear OA(3247, 1027, F32, 24) (dual of [1027, 980, 25]-code), using
- construction XX applied to C1 = C([1022,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([1022,22]) [i] based on
- linear OA(3245, 1023, F32, 23) (dual of [1023, 978, 24]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3245, 1023, F32, 23) (dual of [1023, 978, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3247, 1023, F32, 24) (dual of [1023, 976, 25]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([1022,22]) [i] based on
- 97 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 9 times 0, 1, 25 times 0, 1, 57 times 0) [i] based on linear OA(3247, 1027, F32, 24) (dual of [1027, 980, 25]-code), using
(30, 30+24, 1011980)-Net in Base 32 — Upper bound on s
There is no (30, 54, 1011981)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1897 151368 749853 615009 938667 464252 769884 830900 698961 186230 725469 657211 340964 027937 > 3254 [i]