Best Known (200−20, 200, s)-Nets in Base 2
(200−20, 200, 104857)-Net over F2 — Constructive and digital
Digital (180, 200, 104857)-net over F2, using
- net defined by OOA [i] based on linear OOA(2200, 104857, F2, 20, 20) (dual of [(104857, 20), 2096940, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2200, 1048570, F2, 20) (dual of [1048570, 1048370, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2200, 1048576, F2, 20) (dual of [1048576, 1048376, 21]-code), using
- 1 times truncation [i] based on linear OA(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, 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(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2200, 1048576, F2, 20) (dual of [1048576, 1048376, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2200, 1048570, F2, 20) (dual of [1048570, 1048370, 21]-code), using
(200−20, 200, 174762)-Net over F2 — Digital
Digital (180, 200, 174762)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2200, 174762, F2, 6, 20) (dual of [(174762, 6), 1048372, 21]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2200, 1048572, F2, 20) (dual of [1048572, 1048372, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2200, 1048576, F2, 20) (dual of [1048576, 1048376, 21]-code), using
- 1 times truncation [i] based on linear OA(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, 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(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2200, 1048576, F2, 20) (dual of [1048576, 1048376, 21]-code), using
- OOA 6-folding [i] based on linear OA(2200, 1048572, F2, 20) (dual of [1048572, 1048372, 21]-code), using
(200−20, 200, 4748701)-Net in Base 2 — Upper bound on s
There is no (180, 200, 4748702)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 606939 015821 007457 331120 625317 637385 527703 835820 210923 724434 > 2200 [i]