MinT - Best Known (163, 163+54, s)-Nets in Base 3

Best Known (163, 163+54, s)-Nets in Base 3

(163, 163+54, 328)-Net over F₃ — Constructive and digital

Digital (163, 217, 328)-net over F₃, using

3¹ times duplication [i] based on 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]

(163, 163+54, 925)-Net over F₃ — Digital

Digital (163, 217, 925)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+54, 37300)-Net in Base 3 — Upper bound on s

There is no (163, 217, 37301)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 324564 354785 158940 170948 939042 880993 405378 912809 698338 203582 599625 802440 356137 190497 840551 573503 769483 > 3²¹⁷ [i]