Best Known (55−12, 55, s)-Nets in Base 3
(55−12, 55, 400)-Net over F3 — Constructive and digital
Digital (43, 55, 400)-net over F3, using
- 1 times m-reduction [i] based on digital (43, 56, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 14, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 14, 100)-net over F81, using
(55−12, 55, 845)-Net over F3 — Digital
Digital (43, 55, 845)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(355, 845, F3, 12) (dual of [845, 790, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(355, 1092, F3, 12) (dual of [1092, 1037, 13]-code), using
(55−12, 55, 35378)-Net in Base 3 — Upper bound on s
There is no (43, 55, 35379)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 174 472036 474294 276467 652477 > 355 [i]