Best Known (108, 108+12, s)-Nets in Base 2
(108, 108+12, 174762)-Net over F2 — Constructive and digital
Digital (108, 120, 174762)-net over F2, using
- net defined by OOA [i] based on linear OOA(2120, 174762, F2, 12, 12) (dual of [(174762, 12), 2097024, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2120, 1048572, F2, 12) (dual of [1048572, 1048452, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 1048576, F2, 12) (dual of [1048576, 1048456, 13]-code), using
- 1 times truncation [i] based on linear OA(2121, 1048577, F2, 13) (dual of [1048577, 1048456, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, 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(2121, 1048577, F2, 13) (dual of [1048577, 1048456, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2120, 1048576, F2, 12) (dual of [1048576, 1048456, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2120, 1048572, F2, 12) (dual of [1048572, 1048452, 13]-code), using
(108, 108+12, 262144)-Net over F2 — Digital
Digital (108, 120, 262144)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2120, 262144, F2, 4, 12) (dual of [(262144, 4), 1048456, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2120, 1048576, F2, 12) (dual of [1048576, 1048456, 13]-code), using
- 1 times truncation [i] based on linear OA(2121, 1048577, F2, 13) (dual of [1048577, 1048456, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, 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(2121, 1048577, F2, 13) (dual of [1048577, 1048456, 14]-code), using
- OOA 4-folding [i] based on linear OA(2120, 1048576, F2, 12) (dual of [1048576, 1048456, 13]-code), using
(108, 108+12, 3139213)-Net in Base 2 — Upper bound on s
There is no (108, 120, 3139214)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 329229 877081 755613 664954 023867 287100 > 2120 [i]