Best Known (20, 36, s)-Nets in Base 32
(20, 36, 175)-Net over F32 — Constructive and digital
Digital (20, 36, 175)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (1, 9, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 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 (5, 13, 77)-net over F32, using
(20, 36, 322)-Net in Base 32 — Constructive
(20, 36, 322)-net in base 32, using
- base change [i] based on (14, 30, 322)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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
- (6, 22, 257)-net in base 64, using
- 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- base change [i] based on digital (0, 18, 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, 18, 257)-net over F256, using
- 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- digital (0, 8, 65)-net over F64, using
- (u, u+v)-construction [i] based on
(20, 36, 1078)-Net over F32 — Digital
Digital (20, 36, 1078)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3236, 1078, F32, 16) (dual of [1078, 1042, 17]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 9 times 0, 1, 32 times 0) [i] based on linear OA(3231, 1027, F32, 16) (dual of [1027, 996, 17]-code), using
- construction XX applied to C1 = C([1022,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([1022,14]) [i] based on
- linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3231, 1023, F32, 16) (dual of [1023, 992, 17]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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([1022,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([1022,14]) [i] based on
- 46 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 9 times 0, 1, 32 times 0) [i] based on linear OA(3231, 1027, F32, 16) (dual of [1027, 996, 17]-code), using
(20, 36, 720279)-Net in Base 32 — Upper bound on s
There is no (20, 36, 720280)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1 532505 358814 264025 490574 743562 413038 232966 646585 004922 > 3236 [i]