MinT - Best Known (179−71, 179, s)-Nets in Base 3

Best Known (179−71, 179, s)-Nets in Base 3

(179−71, 179, 148)-Net over F₃ — Constructive and digital

Digital (108, 179, 148)-net over F₃, using

3 times m-reduction [i] based on digital (108, 182, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 91, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(179−71, 179, 174)-Net over F₃ — Digital

Digital (108, 179, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−71, 179, 1822)-Net in Base 3 — Upper bound on s

There is no (108, 179, 1823)-net in base 3, because

1 times m-reduction [i] would yield (108, 178, 1823)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 553773 810817 327624 099540 331016 267014 443579 656568 935025 624751 287379 347042 061046 937147 > 3¹⁷⁸ [i]