Best Known (32, 52, s)-Nets in Base 9
(32, 52, 320)-Net over F9 — Constructive and digital
Digital (32, 52, 320)-net over F9, using
- 2 times m-reduction [i] based on digital (32, 54, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 27, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 27, 160)-net over F81, using
(32, 52, 468)-Net over F9 — Digital
Digital (32, 52, 468)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(952, 468, F9, 20) (dual of [468, 416, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(952, 728, F9, 20) (dual of [728, 676, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(952, 728, F9, 20) (dual of [728, 676, 21]-code), using
(32, 52, 51867)-Net in Base 9 — Upper bound on s
There is no (32, 52, 51868)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 41 745846 016463 768539 522999 480181 988108 745496 074305 > 952 [i]