Best Known (190, 211, s)-Nets in Base 2
(190, 211, 209715)-Net over F2 — Constructive and digital
Digital (190, 211, 209715)-net over F2, using
- net defined by OOA [i] based on linear OOA(2211, 209715, F2, 21, 21) (dual of [(209715, 21), 4403804, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2211, 2097151, F2, 21) (dual of [2097151, 2096940, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using
- an extension Ce(20) of 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(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2211, 2097151, F2, 21) (dual of [2097151, 2096940, 22]-code), using
(190, 211, 299593)-Net over F2 — Digital
Digital (190, 211, 299593)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2211, 299593, F2, 7, 21) (dual of [(299593, 7), 2096940, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2211, 2097151, F2, 21) (dual of [2097151, 2096940, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using
- an extension Ce(20) of 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(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using
- OOA 7-folding [i] based on linear OA(2211, 2097151, F2, 21) (dual of [2097151, 2096940, 22]-code), using
(190, 211, large)-Net in Base 2 — Upper bound on s
There is no (190, 211, large)-net in base 2, because
- 19 times m-reduction [i] would yield (190, 192, large)-net in base 2, but