Best Known (190, 210, s)-Nets in Base 2
(190, 210, 209715)-Net over F2 — Constructive and digital
Digital (190, 210, 209715)-net over F2, using
- net defined by OOA [i] based on linear OOA(2210, 209715, F2, 20, 20) (dual of [(209715, 20), 4194090, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2210, 2097150, F2, 20) (dual of [2097150, 2096940, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2210, 2097150, F2, 20) (dual of [2097150, 2096940, 21]-code), using
(190, 210, 300078)-Net over F2 — Digital
Digital (190, 210, 300078)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2210, 300078, F2, 6, 20) (dual of [(300078, 6), 1800258, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2210, 349525, F2, 6, 20) (dual of [(349525, 6), 2096940, 21]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2210, 2097150, F2, 20) (dual of [2097150, 2096940, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using
- OOA 6-folding [i] based on linear OA(2210, 2097150, F2, 20) (dual of [2097150, 2096940, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(2210, 349525, F2, 6, 20) (dual of [(349525, 6), 2096940, 21]-NRT-code), using
(190, 210, large)-Net in Base 2 — Upper bound on s
There is no (190, 210, large)-net in base 2, because
- 18 times m-reduction [i] would yield (190, 192, large)-net in base 2, but