Best Known (100, 120, s)-Nets in Base 2
(100, 120, 409)-Net over F2 — Constructive and digital
Digital (100, 120, 409)-net over F2, using
- net defined by OOA [i] based on linear OOA(2120, 409, F2, 20, 20) (dual of [(409, 20), 8060, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2120, 4090, F2, 20) (dual of [4090, 3970, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 4096, F2, 20) (dual of [4096, 3976, 21]-code), using
- 1 times truncation [i] based on linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, 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(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 4096, F2, 20) (dual of [4096, 3976, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2120, 4090, F2, 20) (dual of [4090, 3970, 21]-code), using
(100, 120, 1058)-Net over F2 — Digital
Digital (100, 120, 1058)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2120, 1058, F2, 3, 20) (dual of [(1058, 3), 3054, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2120, 1365, F2, 3, 20) (dual of [(1365, 3), 3975, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2120, 4095, F2, 20) (dual of [4095, 3975, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 4096, F2, 20) (dual of [4096, 3976, 21]-code), using
- 1 times truncation [i] based on linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, 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(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 4096, F2, 20) (dual of [4096, 3976, 21]-code), using
- OOA 3-folding [i] based on linear OA(2120, 4095, F2, 20) (dual of [4095, 3975, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(2120, 1365, F2, 3, 20) (dual of [(1365, 3), 3975, 21]-NRT-code), using
(100, 120, 18535)-Net in Base 2 — Upper bound on s
There is no (100, 120, 18536)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 329817 298884 290513 640167 875262 974268 > 2120 [i]