Best Known (233−76, 233, s)-Nets in Base 3
(233−76, 233, 167)-Net over F3 — Constructive and digital
Digital (157, 233, 167)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (9, 47, 19)-net over F3, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- digital (110, 186, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 93, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 93, 74)-net over F9, using
- digital (9, 47, 19)-net over F3, using
(233−76, 233, 389)-Net over F3 — Digital
Digital (157, 233, 389)-net over F3, using
(233−76, 233, 6290)-Net in Base 3 — Upper bound on s
There is no (157, 233, 6291)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1478 454457 226636 577586 520241 705475 479765 465774 843587 336545 058996 906159 628804 546159 895568 269327 615137 119439 123965 > 3233 [i]