Best Known (224−42, 224, s)-Nets in Base 3
(224−42, 224, 896)-Net over F3 — Constructive and digital
Digital (182, 224, 896)-net over F3, using
- t-expansion [i] based on digital (181, 224, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 56, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 56, 224)-net over F81, using
(224−42, 224, 3565)-Net over F3 — Digital
Digital (182, 224, 3565)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3224, 3565, F3, 42) (dual of [3565, 3341, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3224, 6561, F3, 42) (dual of [6561, 6337, 43]-code), using
- 1 times truncation [i] based on linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3224, 6561, F3, 42) (dual of [6561, 6337, 43]-code), using
(224−42, 224, 533014)-Net in Base 3 — Upper bound on s
There is no (182, 224, 533015)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 75017 882775 483375 805148 147918 513975 956061 513262 456521 076298 955199 315245 664810 059276 682130 586852 395683 426759 > 3224 [i]