MinT - Best Known (162, 162+54, s)-Nets in Base 3

Best Known (162, 162+54, s)-Nets in Base 3

(162, 162+54, 328)-Net over F₃ — Constructive and digital

Digital (162, 216, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 54, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(162, 162+54, 905)-Net over F₃ — Digital

Digital (162, 216, 905)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+54, 35811)-Net in Base 3 — Upper bound on s

There is no (162, 216, 35812)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 435882 034737 323408 301757 443627 721459 597522 422688 558141 549656 202357 837286 692560 133143 136547 021903 602417 > 3²¹⁶ [i]