Best Known (102−12, 102, s)-Nets in Base 2
(102−12, 102, 21845)-Net over F2 — Constructive and digital
Digital (90, 102, 21845)-net over F2, using
- net defined by OOA [i] based on linear OOA(2102, 21845, F2, 12, 12) (dual of [(21845, 12), 262038, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2102, 131070, F2, 12) (dual of [131070, 130968, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2102, 131072, F2, 12) (dual of [131072, 130970, 13]-code), using
- 1 times truncation [i] based on linear OA(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, 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(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2102, 131072, F2, 12) (dual of [131072, 130970, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2102, 131070, F2, 12) (dual of [131070, 130968, 13]-code), using
(102−12, 102, 32768)-Net over F2 — Digital
Digital (90, 102, 32768)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2102, 32768, F2, 4, 12) (dual of [(32768, 4), 130970, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2102, 131072, F2, 12) (dual of [131072, 130970, 13]-code), using
- 1 times truncation [i] based on linear OA(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, 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(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using
- OOA 4-folding [i] based on linear OA(2102, 131072, F2, 12) (dual of [131072, 130970, 13]-code), using
(102−12, 102, 392394)-Net in Base 2 — Upper bound on s
There is no (90, 102, 392395)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5 070662 874650 160947 855090 077370 > 2102 [i]