Best Known (44, 44+28, s)-Nets in Base 7
(44, 44+28, 116)-Net over F7 — Constructive and digital
Digital (44, 72, 116)-net over F7, using
- trace code for nets [i] based on digital (8, 36, 58)-net over F49, using
- net from sequence [i] based on digital (8, 57)-sequence over F49, using
(44, 44+28, 343)-Net over F7 — Digital
Digital (44, 72, 343)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(772, 343, F7, 28) (dual of [343, 271, 29]-code), using
- 1 times truncation [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 344 | 76−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
(44, 44+28, 22353)-Net in Base 7 — Upper bound on s
There is no (44, 72, 22354)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 7 032089 970192 836023 865376 267862 695164 253935 633484 118752 121213 > 772 [i]