MinT - Best Known (179−69, 179, s)-Nets in Base 3

Best Known (179−69, 179, s)-Nets in Base 3

(179−69, 179, 148)-Net over F₃ — Constructive and digital

Digital (110, 179, 148)-net over F₃, using

7 times m-reduction [i] based on digital (110, 186, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 93, 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]

(179−69, 179, 189)-Net over F₃ — Digital

Digital (110, 179, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−69, 179, 2096)-Net in Base 3 — Upper bound on s

There is no (110, 179, 2097)-net in base 3, because

1 times m-reduction [i] would yield (110, 178, 2097)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 545067 935909 384548 836248 796454 142805 990340 754516 319502 057818 646272 805191 217480 176233 > 3¹⁷⁸ [i]