MinT - Best Known (116−39, 116, s)-Nets in Base 3

Best Known (116−39, 116, s)-Nets in Base 3

(116−39, 116, 148)-Net over F₃ — Constructive and digital

Digital (77, 116, 148)-net over F₃, using

4 times m-reduction [i] based on digital (77, 120, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 60, 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]

(116−39, 116, 197)-Net over F₃ — Digital

Digital (77, 116, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−39, 116, 3043)-Net in Base 3 — Upper bound on s

There is no (77, 116, 3044)-net in base 3, because

1 times m-reduction [i] would yield (77, 115, 3044)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 409613 023491 966507 962844 643947 790270 850469 662755 766065 > 3¹¹⁵ [i]