MinT - Best Known (179−45, 179, s)-Nets in Base 3

Best Known (179−45, 179, s)-Nets in Base 3

(179−45, 179, 288)-Net over F₃ — Constructive and digital

Digital (134, 179, 288)-net over F₃, using

t-expansion [i] based on digital (133, 179, 288)-net over F₃, using
- 4 times m-reduction [i] based on digital (133, 183, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 61, 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]

(179−45, 179, 760)-Net over F₃ — Digital

Digital (134, 179, 760)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−45, 179, 32800)-Net in Base 3 — Upper bound on s

There is no (134, 179, 32801)-net in base 3, because

1 times m-reduction [i] would yield (134, 178, 32801)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 465800 925787 715740 538895 915402 602806 889393 286153 299753 140825 108071 310933 798324 911449 > 3¹⁷⁸ [i]