Best Known (105, 105+14, s)-Nets in Base 2
(105, 105+14, 18724)-Net over F2 — Constructive and digital
Digital (105, 119, 18724)-net over F2, using
- net defined by OOA [i] based on linear OOA(2119, 18724, F2, 14, 14) (dual of [(18724, 14), 262017, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2119, 131068, F2, 14) (dual of [131068, 130949, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2119, 131071, F2, 14) (dual of [131071, 130952, 15]-code), using
- 1 times truncation [i] based on linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2119, 131071, F2, 14) (dual of [131071, 130952, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2119, 131068, F2, 14) (dual of [131068, 130949, 15]-code), using
(105, 105+14, 29111)-Net over F2 — Digital
Digital (105, 119, 29111)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2119, 29111, F2, 4, 14) (dual of [(29111, 4), 116325, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 32767, F2, 4, 14) (dual of [(32767, 4), 130949, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2119, 131068, F2, 14) (dual of [131068, 130949, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2119, 131071, F2, 14) (dual of [131071, 130952, 15]-code), using
- 1 times truncation [i] based on linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2119, 131071, F2, 14) (dual of [131071, 130952, 15]-code), using
- OOA 4-folding [i] based on linear OA(2119, 131068, F2, 14) (dual of [131068, 130949, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(2119, 32767, F2, 4, 14) (dual of [(32767, 4), 130949, 15]-NRT-code), using
(105, 105+14, 443015)-Net in Base 2 — Upper bound on s
There is no (105, 119, 443016)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 664620 854804 661904 954338 004213 982815 > 2119 [i]