Best Known (126−12, 126, s)-Nets in Base 2
(126−12, 126, 349525)-Net over F2 — Constructive and digital
Digital (114, 126, 349525)-net over F2, using
- net defined by OOA [i] based on linear OOA(2126, 349525, F2, 12, 12) (dual of [(349525, 12), 4194174, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2126, 2097150, F2, 12) (dual of [2097150, 2097024, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2126, 2097152, F2, 12) (dual of [2097152, 2097026, 13]-code), using
- 1 times truncation [i] based on linear OA(2127, 2097153, F2, 13) (dual of [2097153, 2097026, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2127, 2097153, F2, 13) (dual of [2097153, 2097026, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2126, 2097152, F2, 12) (dual of [2097152, 2097026, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2126, 2097150, F2, 12) (dual of [2097150, 2097024, 13]-code), using
(126−12, 126, 524288)-Net over F2 — Digital
Digital (114, 126, 524288)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2126, 524288, F2, 4, 12) (dual of [(524288, 4), 2097026, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2126, 2097152, F2, 12) (dual of [2097152, 2097026, 13]-code), using
- 1 times truncation [i] based on linear OA(2127, 2097153, F2, 13) (dual of [2097153, 2097026, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2127, 2097153, F2, 13) (dual of [2097153, 2097026, 14]-code), using
- OOA 4-folding [i] based on linear OA(2126, 2097152, F2, 12) (dual of [2097152, 2097026, 13]-code), using
(126−12, 126, 6278435)-Net in Base 2 — Upper bound on s
There is no (114, 126, 6278436)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 85 070671 485522 119560 251172 936060 117288 > 2126 [i]