MinT - Best Known (116, 116+82, s)-Nets in Base 3

Best Known (116, 116+82, s)-Nets in Base 3

(116, 116+82, 148)-Net over F₃ — Constructive and digital

Digital (116, 198, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 99, 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, 116+82, 168)-Net over F₃ — Digital

Digital (116, 198, 168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+82, 1585)-Net in Base 3 — Upper bound on s

There is no (116, 198, 1586)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29831 150661 991571 998490 169889 311495 562823 444787 897184 408134 663031 233623 862201 448418 569733 318997 > 3¹⁹⁸ [i]