Best Known (50−26, 50, s)-Nets in Base 32
(50−26, 50, 162)-Net over F32 — Constructive and digital
Digital (24, 50, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (24, 52, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 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 (7, 35, 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 (3, 17, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(50−26, 50, 288)-Net in Base 32 — Constructive
(24, 50, 288)-net in base 32, using
- 321 times duplication [i] based on (23, 49, 288)-net in base 32, using
- base change [i] based on digital (9, 35, 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, 35, 288)-net over F128, using
(50−26, 50, 356)-Net over F32 — Digital
Digital (24, 50, 356)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3250, 356, F32, 26) (dual of [356, 306, 27]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(3249, 345, F32, 26) (dual of [345, 296, 27]-code), using
- construction XX applied to C1 = C([340,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([340,24]) [i] based on
- linear OA(3247, 341, F32, 25) (dual of [341, 294, 26]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3247, 341, F32, 25) (dual of [341, 294, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3249, 341, F32, 26) (dual of [341, 292, 27]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3245, 341, F32, 24) (dual of [341, 296, 25]-code), using the expurgated narrow-sense BCH-code C(I) with length 341 | 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([340,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([340,24]) [i] based on
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(3249, 345, F32, 26) (dual of [345, 296, 27]-code), using
(50−26, 50, 112475)-Net in Base 32 — Upper bound on s
There is no (24, 50, 112476)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1809 348125 848975 972882 957799 598594 878247 998250 615085 386997 870134 101938 109492 > 3250 [i]