MinT - Best Known (162−61, 162, s)-Nets in Base 3

Best Known (162−61, 162, s)-Nets in Base 3

(162−61, 162, 148)-Net over F₃ — Constructive and digital

Digital (101, 162, 148)-net over F₃, using

6 times m-reduction [i] based on digital (101, 168, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 84, 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]

(162−61, 162, 185)-Net over F₃ — Digital

Digital (101, 162, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−61, 162, 2159)-Net in Base 3 — Upper bound on s

There is no (101, 162, 2160)-net in base 3, because

1 times m-reduction [i] would yield (101, 161, 2160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65555 200546 926704 054880 386323 848458 199772 825462 705352 761708 473534 065243 069345 > 3¹⁶¹ [i]