Best Known (162−36, 162, s)-Nets in Base 3
(162−36, 162, 600)-Net over F3 — Constructive and digital
Digital (126, 162, 600)-net over F3, using
- 32 times duplication [i] based on digital (124, 160, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F81, using
(162−36, 162, 1141)-Net over F3 — Digital
Digital (126, 162, 1141)-net over F3, using
(162−36, 162, 74317)-Net in Base 3 — Upper bound on s
There is no (126, 162, 74318)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 196667 014697 274508 485998 233637 570007 631553 384960 607527 773680 217285 407650 932605 > 3162 [i]