Best Known (140, 180, s)-Nets in Base 4
(140, 180, 1048)-Net over F4 — Constructive and digital
Digital (140, 180, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 45, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(140, 180, 3403)-Net over F4 — Digital
Digital (140, 180, 3403)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4180, 3403, F4, 40) (dual of [3403, 3223, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 4096, F4, 40) (dual of [4096, 3916, 41]-code), using
- 1 times truncation [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 4096, F4, 40) (dual of [4096, 3916, 41]-code), using
(140, 180, 725629)-Net in Base 4 — Upper bound on s
There is no (140, 180, 725630)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 348543 363610 649732 243060 829375 778369 160142 163725 302100 270021 200789 047045 788950 178856 694244 878073 268751 329871 > 4180 [i]