Best Known (198, 198+32, s)-Nets in Base 2
(198, 198+32, 1026)-Net over F2 — Constructive and digital
Digital (198, 230, 1026)-net over F2, using
- net defined by OOA [i] based on linear OOA(2230, 1026, F2, 32, 32) (dual of [(1026, 32), 32602, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2230, 16416, F2, 32) (dual of [16416, 16186, 33]-code), using
- 1 times truncation [i] based on linear OA(2231, 16417, F2, 33) (dual of [16417, 16186, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2225, 16385, F2, 33) (dual of [16385, 16160, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2197, 16385, F2, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2231, 16417, F2, 33) (dual of [16417, 16186, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(2230, 16416, F2, 32) (dual of [16416, 16186, 33]-code), using
(198, 198+32, 3576)-Net over F2 — Digital
Digital (198, 230, 3576)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2230, 3576, F2, 4, 32) (dual of [(3576, 4), 14074, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2230, 4104, F2, 4, 32) (dual of [(4104, 4), 16186, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2230, 16416, F2, 32) (dual of [16416, 16186, 33]-code), using
- 1 times truncation [i] based on linear OA(2231, 16417, F2, 33) (dual of [16417, 16186, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2225, 16385, F2, 33) (dual of [16385, 16160, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2197, 16385, F2, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2231, 16417, F2, 33) (dual of [16417, 16186, 34]-code), using
- OOA 4-folding [i] based on linear OA(2230, 16416, F2, 32) (dual of [16416, 16186, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(2230, 4104, F2, 4, 32) (dual of [(4104, 4), 16186, 33]-NRT-code), using
(198, 198+32, 144468)-Net in Base 2 — Upper bound on s
There is no (198, 230, 144469)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1725 461236 904330 076677 202527 219760 601381 961826 717714 045489 872143 462505 > 2230 [i]