Best Known (119, 119+14, s)-Nets in Base 2
(119, 119+14, 74898)-Net over F2 — Constructive and digital
Digital (119, 133, 74898)-net over F2, using
- net defined by OOA [i] based on linear OOA(2133, 74898, F2, 14, 14) (dual of [(74898, 14), 1048439, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2133, 524286, F2, 14) (dual of [524286, 524153, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2133, 524287, F2, 14) (dual of [524287, 524154, 15]-code), using
- 1 times truncation [i] based on linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2133, 524287, F2, 14) (dual of [524287, 524154, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2133, 524286, F2, 14) (dual of [524286, 524153, 15]-code), using
(119, 119+14, 104857)-Net over F2 — Digital
Digital (119, 133, 104857)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2133, 104857, F2, 5, 14) (dual of [(104857, 5), 524152, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2133, 524285, F2, 14) (dual of [524285, 524152, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2133, 524287, F2, 14) (dual of [524287, 524154, 15]-code), using
- 1 times truncation [i] based on linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2133, 524287, F2, 14) (dual of [524287, 524154, 15]-code), using
- OOA 5-folding [i] based on linear OA(2133, 524285, F2, 14) (dual of [524285, 524152, 15]-code), using
(119, 119+14, 1772091)-Net in Base 2 — Upper bound on s
There is no (119, 133, 1772092)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 10889 062074 835304 816644 067412 360121 123370 > 2133 [i]