Best Known (34, 34+26, s)-Nets in Base 32
(34, 34+26, 228)-Net over F32 — Constructive and digital
Digital (34, 60, 228)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 108)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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 (3, 16, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (1, 7, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 37, 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 (10, 23, 108)-net over F32, using
(34, 34+26, 338)-Net in Base 32 — Constructive
(34, 60, 338)-net in base 32, using
- base change [i] based on (24, 50, 338)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 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
- (10, 36, 258)-net in base 64, using
- base change [i] based on digital (1, 27, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 27, 258)-net over F256, using
- digital (1, 14, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(34, 34+26, 1363)-Net over F32 — Digital
Digital (34, 60, 1363)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3260, 1363, F32, 26) (dual of [1363, 1303, 27]-code), using
- 327 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 47 times 0, 1, 94 times 0, 1, 150 times 0) [i] based on linear OA(3251, 1027, F32, 26) (dual of [1027, 976, 27]-code), using
- construction XX applied to C1 = C([1022,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([1022,24]) [i] based on
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3247, 1023, F32, 24) (dual of [1023, 976, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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([1022,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([1022,24]) [i] based on
- 327 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 47 times 0, 1, 94 times 0, 1, 150 times 0) [i] based on linear OA(3251, 1027, F32, 26) (dual of [1027, 976, 27]-code), using
(34, 34+26, 1617665)-Net in Base 32 — Upper bound on s
There is no (34, 60, 1617666)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 037038 590981 524980 556424 653571 438670 538482 075353 666872 929746 591047 919859 743148 840581 641792 > 3260 [i]