Best Known (32, 32+20, s)-Nets in Base 7
(32, 32+20, 113)-Net over F7 — Constructive and digital
Digital (32, 52, 113)-net over F7, using
- 1 times m-reduction [i] based on digital (32, 53, 113)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 13)-net over F7, using
- 2 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (21, 42, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 21, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 21, 50)-net over F49, using
- digital (1, 11, 13)-net over F7, using
- (u, u+v)-construction [i] based on
(32, 32+20, 302)-Net over F7 — Digital
Digital (32, 52, 302)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(752, 302, F7, 20) (dual of [302, 250, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using
(32, 32+20, 18715)-Net in Base 7 — Upper bound on s
There is no (32, 52, 18716)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 88 167876 701558 892002 837531 966298 309990 711529 > 752 [i]