Best Known (168, 168+40, s)-Nets in Base 3
(168, 168+40, 692)-Net over F3 — Constructive and digital
Digital (168, 208, 692)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 20, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (148, 188, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 47, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 47, 172)-net over F81, using
- digital (0, 20, 4)-net over F3, using
(168, 168+40, 2948)-Net over F3 — Digital
Digital (168, 208, 2948)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3208, 2948, F3, 40) (dual of [2948, 2740, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 3281, F3, 40) (dual of [3281, 3073, 41]-code), using
(168, 168+40, 380465)-Net in Base 3 — Upper bound on s
There is no (168, 208, 380466)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1742 759677 106197 609981 585810 706371 598960 697638 631791 052729 820766 508725 808700 355969 736741 488423 477193 > 3208 [i]