MinT - Best Known (117, 117+73, s)-Nets in Base 3

Best Known (117, 117+73, s)-Nets in Base 3

(117, 117+73, 156)-Net over F₃ — Constructive and digital

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+73, 201)-Net over F₃ — Digital

Digital (117, 190, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+73, 2248)-Net in Base 3 — Upper bound on s

There is no (117, 190, 2249)-net in base 3, because

1 times m-reduction [i] would yield (117, 189, 2249)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 518668 581343 750947 233300 127474 160842 907699 218009 558330 713049 679422 843582 110335 161534 767249 > 3¹⁸⁹ [i]