Best Known (30, 48, s)-Nets in Base 7
(30, 48, 115)-Net over F7 — Constructive and digital
Digital (30, 48, 115)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (20, 38, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 19, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- trace code for nets [i] based on digital (1, 19, 51)-net over F49, using
- digital (1, 10, 13)-net over F7, using
(30, 48, 335)-Net over F7 — Digital
Digital (30, 48, 335)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(748, 335, F7, 18) (dual of [335, 287, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(748, 342, F7, 18) (dual of [342, 294, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(748, 342, F7, 18) (dual of [342, 294, 19]-code), using
(30, 48, 22216)-Net in Base 7 — Upper bound on s
There is no (30, 48, 22217)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 36705 772845 878518 575338 671069 084640 462455 > 748 [i]