Best Known (140, 160, s)-Nets in Base 2
(140, 160, 6553)-Net over F2 — Constructive and digital
Digital (140, 160, 6553)-net over F2, using
- net defined by OOA [i] based on linear OOA(2160, 6553, F2, 20, 20) (dual of [(6553, 20), 130900, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2160, 65530, F2, 20) (dual of [65530, 65370, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 65536, F2, 20) (dual of [65536, 65376, 21]-code), using
- 1 times truncation [i] based on linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 65536, F2, 20) (dual of [65536, 65376, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2160, 65530, F2, 20) (dual of [65530, 65370, 21]-code), using
(140, 160, 12990)-Net over F2 — Digital
Digital (140, 160, 12990)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2160, 12990, F2, 5, 20) (dual of [(12990, 5), 64790, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2160, 13107, F2, 5, 20) (dual of [(13107, 5), 65375, 21]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2160, 65535, F2, 20) (dual of [65535, 65375, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 65536, F2, 20) (dual of [65536, 65376, 21]-code), using
- 1 times truncation [i] based on linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 65536, F2, 20) (dual of [65536, 65376, 21]-code), using
- OOA 5-folding [i] based on linear OA(2160, 65535, F2, 20) (dual of [65535, 65375, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(2160, 13107, F2, 5, 20) (dual of [(13107, 5), 65375, 21]-NRT-code), using
(140, 160, 296780)-Net in Base 2 — Upper bound on s
There is no (140, 160, 296781)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 461537 899100 311317 374855 306584 790404 657368 911598 > 2160 [i]