Best Known (174−24, 174, s)-Nets in Base 2
(174−24, 174, 1368)-Net over F2 — Constructive and digital
Digital (150, 174, 1368)-net over F2, using
- net defined by OOA [i] based on linear OOA(2174, 1368, F2, 24, 24) (dual of [(1368, 24), 32658, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2174, 16416, F2, 24) (dual of [16416, 16242, 25]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- OA 12-folding and stacking [i] based on linear OA(2174, 16416, F2, 24) (dual of [16416, 16242, 25]-code), using
(174−24, 174, 3887)-Net over F2 — Digital
Digital (150, 174, 3887)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2174, 3887, F2, 4, 24) (dual of [(3887, 4), 15374, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2174, 4104, F2, 4, 24) (dual of [(4104, 4), 16242, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2174, 16416, F2, 24) (dual of [16416, 16242, 25]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(2175, 16417, F2, 25) (dual of [16417, 16242, 26]-code), using
- OOA 4-folding [i] based on linear OA(2174, 16416, F2, 24) (dual of [16416, 16242, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(2174, 4104, F2, 4, 24) (dual of [(4104, 4), 16242, 25]-NRT-code), using
(174−24, 174, 122527)-Net in Base 2 — Upper bound on s
There is no (150, 174, 122528)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 23945 913292 335616 710658 708146 461831 203135 922849 391997 > 2174 [i]