MinT - Best Known (83−25, 83, s)-Nets in Base 3

Best Known (83−25, 83, s)-Nets in Base 3

(83−25, 83, 144)-Net over F₃ — Constructive and digital

Digital (58, 83, 144)-net over F₃, using

1 times m-reduction [i] based on digital (58, 84, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 28, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]

(83−25, 83, 219)-Net over F₃ — Digital

Digital (58, 83, 219)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−25, 83, 4804)-Net in Base 3 — Upper bound on s

There is no (58, 83, 4805)-net in base 3, because

1 times m-reduction [i] would yield (58, 82, 4805)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1332 874674 223696 466580 956275 524373 705009 > 3⁸² [i]