Best Known (175−24, 175, s)-Nets in Base 2
(175−24, 175, 1368)-Net over F2 — Constructive and digital
Digital (151, 175, 1368)-net over F2, using
- t-expansion [i] based on digital (150, 175, 1368)-net over F2, using
- net defined by OOA [i] based on linear OOA(2175, 1368, F2, 25, 25) (dual of [(1368, 25), 34025, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2141, 16385, F2, 21) (dual of [16385, 16244, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- net defined by OOA [i] based on linear OOA(2175, 1368, F2, 25, 25) (dual of [(1368, 25), 34025, 26]-NRT-code), using
(175−24, 175, 4032)-Net over F2 — Digital
Digital (151, 175, 4032)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2175, 4032, F2, 4, 24) (dual of [(4032, 4), 15953, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2175, 4104, F2, 4, 24) (dual of [(4104, 4), 16241, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(2175, 4104, F2, 4, 25) (dual of [(4104, 4), 16241, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2175, 16416, F2, 25) (dual of [16416, 16241, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2141, 16385, F2, 21) (dual of [16385, 16244, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- OOA 4-folding [i] based on linear OA(2175, 16416, F2, 25) (dual of [16416, 16241, 26]-code), using
- strength reduction [i] based on linear OOA(2175, 4104, F2, 4, 25) (dual of [(4104, 4), 16241, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2175, 4104, F2, 4, 24) (dual of [(4104, 4), 16241, 25]-NRT-code), using
(175−24, 175, 129814)-Net in Base 2 — Upper bound on s
There is no (151, 175, 129815)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 47892 116521 897540 175030 909695 972153 628553 479323 835878 > 2175 [i]