MinT - Best Known (117, 117+64, s)-Nets in Base 3

Best Known (117, 117+64, s)-Nets in Base 3

(117, 117+64, 156)-Net over F₃ — Constructive and digital

Digital (117, 181, 156)-net over F₃, using

9 times m-reduction [i] based on digital (117, 190, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 95, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(117, 117+64, 244)-Net over F₃ — Digital

Digital (117, 181, 244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+64, 3164)-Net in Base 3 — Upper bound on s

There is no (117, 181, 3165)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 230 047727 258666 985300 549852 434721 089254 684409 743055 771892 738589 755979 955439 708495 772545 > 3¹⁸¹ [i]