Best Known (121, 143, s)-Nets in Base 2
(121, 143, 744)-Net over F2 — Constructive and digital
Digital (121, 143, 744)-net over F2, using
- net defined by OOA [i] based on linear OOA(2143, 744, F2, 22, 22) (dual of [(744, 22), 16225, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2143, 8184, F2, 22) (dual of [8184, 8041, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2143, 8191, F2, 22) (dual of [8191, 8048, 23]-code), using
- 1 times truncation [i] based on linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2143, 8191, F2, 22) (dual of [8191, 8048, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2143, 8184, F2, 22) (dual of [8184, 8041, 23]-code), using
(121, 143, 2047)-Net over F2 — Digital
Digital (121, 143, 2047)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2143, 2047, F2, 4, 22) (dual of [(2047, 4), 8045, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2143, 8188, F2, 22) (dual of [8188, 8045, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2143, 8191, F2, 22) (dual of [8191, 8048, 23]-code), using
- 1 times truncation [i] based on linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2143, 8191, F2, 22) (dual of [8191, 8048, 23]-code), using
- OOA 4-folding [i] based on linear OA(2143, 8188, F2, 22) (dual of [8188, 8045, 23]-code), using
(121, 143, 40200)-Net in Base 2 — Upper bound on s
There is no (121, 143, 40201)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11 151937 449512 016429 291162 311856 117136 985128 > 2143 [i]