MinT - Best Known (83, 83+37, s)-Nets in Base 3

Best Known (83, 83+37, s)-Nets in Base 3

(83, 83+37, 156)-Net over F₃ — Constructive and digital

Digital (83, 120, 156)-net over F₃, using

2 times m-reduction [i] based on digital (83, 122, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 61, 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]

(83, 83+37, 265)-Net over F₃ — Digital

Digital (83, 120, 265)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+37, 5370)-Net in Base 3 — Upper bound on s

There is no (83, 120, 5371)-net in base 3, because

1 times m-reduction [i] would yield (83, 119, 5371)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 600 601502 849225 101292 307902 595332 066455 811171 405631 881077 > 3¹¹⁹ [i]