Best Known (183−27, 183, s)-Nets in Base 2
(183−27, 183, 1260)-Net over F2 — Constructive and digital
Digital (156, 183, 1260)-net over F2, using
- net defined by OOA [i] based on linear OOA(2183, 1260, F2, 27, 27) (dual of [(1260, 27), 33837, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2183, 16381, F2, 27) (dual of [16381, 16198, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2183, 16381, F2, 27) (dual of [16381, 16198, 28]-code), using
(183−27, 183, 3061)-Net over F2 — Digital
Digital (156, 183, 3061)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2183, 3061, F2, 5, 27) (dual of [(3061, 5), 15122, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2183, 3276, F2, 5, 27) (dual of [(3276, 5), 16197, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2183, 16380, F2, 27) (dual of [16380, 16197, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using
- OOA 5-folding [i] based on linear OA(2183, 16380, F2, 27) (dual of [16380, 16197, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2183, 3276, F2, 5, 27) (dual of [(3276, 5), 16197, 28]-NRT-code), using
(183−27, 183, 92840)-Net in Base 2 — Upper bound on s
There is no (156, 183, 92841)-net in base 2, because
- 1 times m-reduction [i] would yield (156, 182, 92841)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 6 130450 755471 694060 027885 256886 842011 144264 410594 544272 > 2182 [i]