MinT - Best Known (83, 83+52, s)-Nets in Base 3

Best Known (83, 83+52, s)-Nets in Base 3

(83, 83+52, 128)-Net over F₃ — Constructive and digital

Digital (83, 135, 128)-net over F₃, using

5 times m-reduction [i] based on digital (83, 140, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 70, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(83, 83+52, 149)-Net over F₃ — Digital

Digital (83, 135, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+52, 1558)-Net in Base 3 — Upper bound on s

There is no (83, 135, 1559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26130 464907 429820 928191 599326 379834 254409 979365 624967 943338 187133 > 3¹³⁵ [i]