Best Known (183, 211, s)-Nets in Base 2
(183, 211, 2341)-Net over F2 — Constructive and digital
Digital (183, 211, 2341)-net over F2, using
- net defined by OOA [i] based on linear OOA(2211, 2341, F2, 28, 28) (dual of [(2341, 28), 65337, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2211, 32774, F2, 28) (dual of [32774, 32563, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 32783, F2, 28) (dual of [32783, 32572, 29]-code), using
- 1 times truncation [i] based on linear OA(2212, 32784, F2, 29) (dual of [32784, 32572, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2211, 32768, F2, 29) (dual of [32768, 32557, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2212, 32784, F2, 29) (dual of [32784, 32572, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 32783, F2, 28) (dual of [32783, 32572, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2211, 32774, F2, 28) (dual of [32774, 32563, 29]-code), using
(183, 211, 5933)-Net over F2 — Digital
Digital (183, 211, 5933)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2211, 5933, F2, 5, 28) (dual of [(5933, 5), 29454, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2211, 6556, F2, 5, 28) (dual of [(6556, 5), 32569, 29]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2211, 32780, F2, 28) (dual of [32780, 32569, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 32783, F2, 28) (dual of [32783, 32572, 29]-code), using
- 1 times truncation [i] based on linear OA(2212, 32784, F2, 29) (dual of [32784, 32572, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2211, 32768, F2, 29) (dual of [32768, 32557, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2212, 32784, F2, 29) (dual of [32784, 32572, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2211, 32783, F2, 28) (dual of [32783, 32572, 29]-code), using
- OOA 5-folding [i] based on linear OA(2211, 32780, F2, 28) (dual of [32780, 32569, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2211, 6556, F2, 5, 28) (dual of [(6556, 5), 32569, 29]-NRT-code), using
(183, 211, 208145)-Net in Base 2 — Upper bound on s
There is no (183, 211, 208146)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3291 117479 597995 028274 013757 441823 085402 151221 316769 265636 089736 > 2211 [i]