Best Known (196, 196+29, s)-Nets in Base 2
(196, 196+29, 4681)-Net over F2 — Constructive and digital
Digital (196, 225, 4681)-net over F2, using
- net defined by OOA [i] based on linear OOA(2225, 4681, F2, 29, 29) (dual of [(4681, 29), 135524, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2225, 65535, F2, 29) (dual of [65535, 65310, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2225, 65535, F2, 29) (dual of [65535, 65310, 30]-code), using
(196, 196+29, 9362)-Net over F2 — Digital
Digital (196, 225, 9362)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2225, 9362, F2, 7, 29) (dual of [(9362, 7), 65309, 30]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2225, 65534, F2, 29) (dual of [65534, 65309, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using
- OOA 7-folding [i] based on linear OA(2225, 65534, F2, 29) (dual of [65534, 65309, 30]-code), using
(196, 196+29, 396200)-Net in Base 2 — Upper bound on s
There is no (196, 225, 396201)-net in base 2, because
- 1 times m-reduction [i] would yield (196, 224, 396201)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 26 960265 794832 602542 230895 760800 078179 341803 045566 104326 538706 177424 > 2224 [i]