MinT - Best Known (117, 117+82, s)-Nets in Base 3

Best Known (117, 117+82, s)-Nets in Base 3

(117, 117+82, 148)-Net over F₃ — Constructive and digital

Digital (117, 199, 148)-net over F₃, using

1 times m-reduction [i] based on digital (117, 200, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 100, 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]

(117, 117+82, 171)-Net over F₃ — Digital

Digital (117, 199, 171)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+82, 1629)-Net in Base 3 — Upper bound on s

There is no (117, 199, 1630)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 89164 880300 684208 827385 838023 463300 096860 129160 521833 288158 854183 470258 304658 499403 892037 935341 > 3¹⁹⁹ [i]