Best Known (114−12, 114, s)-Nets in Base 2
(114−12, 114, 87381)-Net over F2 — Constructive and digital
Digital (102, 114, 87381)-net over F2, using
- net defined by OOA [i] based on linear OOA(2114, 87381, F2, 12, 12) (dual of [(87381, 12), 1048458, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2114, 524286, F2, 12) (dual of [524286, 524172, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2114, 524288, F2, 12) (dual of [524288, 524174, 13]-code), using
- 1 times truncation [i] based on linear OA(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, 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(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2114, 524288, F2, 12) (dual of [524288, 524174, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2114, 524286, F2, 12) (dual of [524286, 524172, 13]-code), using
(114−12, 114, 131072)-Net over F2 — Digital
Digital (102, 114, 131072)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2114, 131072, F2, 4, 12) (dual of [(131072, 4), 524174, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2114, 524288, F2, 12) (dual of [524288, 524174, 13]-code), using
- 1 times truncation [i] based on linear OA(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, 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(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using
- OOA 4-folding [i] based on linear OA(2114, 524288, F2, 12) (dual of [524288, 524174, 13]-code), using
(114−12, 114, 1569602)-Net in Base 2 — Upper bound on s
There is no (102, 114, 1569603)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 20769 236676 332356 056484 013855 397568 > 2114 [i]