MinT - Best Known (163, 163+55, s)-Nets in Base 3

Best Known (163, 163+55, s)-Nets in Base 3

(163, 163+55, 288)-Net over F₃ — Constructive and digital

Digital (163, 218, 288)-net over F₃, using

10 times m-reduction [i] based on digital (163, 228, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 76, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(163, 163+55, 880)-Net over F₃ — Digital

Digital (163, 218, 880)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+55, 37300)-Net in Base 3 — Upper bound on s

There is no (163, 218, 37301)-net in base 3, because

1 times m-reduction [i] would yield (163, 217, 37301)-net in base 3, but
- 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]