MinT - Best Known (116, 116+75, s)-Nets in Base 3

Best Known (116, 116+75, s)-Nets in Base 3

(116, 116+75, 148)-Net over F₃ — Constructive and digital

Digital (116, 191, 148)-net over F₃, using

7 times m-reduction [i] based on 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+75, 189)-Net over F₃ — Digital

Digital (116, 191, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+75, 2028)-Net in Base 3 — Upper bound on s

There is no (116, 191, 2029)-net in base 3, because

1 times m-reduction [i] would yield (116, 190, 2029)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 500178 984521 187873 568252 062543 782029 597939 345777 719818 839096 410493 683517 696066 556063 213675 > 3¹⁹⁰ [i]