Best Known (114, 114+30, s)-Nets in Base 5
(114, 114+30, 1041)-Net over F5 — Constructive and digital
Digital (114, 144, 1041)-net over F5, using
- net defined by OOA [i] based on linear OOA(5144, 1041, F5, 30, 30) (dual of [(1041, 30), 31086, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(5144, 15615, F5, 30) (dual of [15615, 15471, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 15625, F5, 30) (dual of [15625, 15481, 31]-code), using
- 1 times truncation [i] based on linear OA(5145, 15626, F5, 31) (dual of [15626, 15481, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5145, 15626, F5, 31) (dual of [15626, 15481, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 15625, F5, 30) (dual of [15625, 15481, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(5144, 15615, F5, 30) (dual of [15615, 15471, 31]-code), using
(114, 114+30, 10468)-Net over F5 — Digital
Digital (114, 144, 10468)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 10468, F5, 30) (dual of [10468, 10324, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 15625, F5, 30) (dual of [15625, 15481, 31]-code), using
- 1 times truncation [i] based on linear OA(5145, 15626, F5, 31) (dual of [15626, 15481, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5145, 15626, F5, 31) (dual of [15626, 15481, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 15625, F5, 30) (dual of [15625, 15481, 31]-code), using
(114, 114+30, 8237930)-Net in Base 5 — Upper bound on s
There is no (114, 144, 8237931)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 44841 590694 312365 660468 132534 580709 154289 077785 928262 011269 269948 893664 972306 091966 198365 995753 391285 > 5144 [i]