MinT - Best Known (83−39, 83, s)-Nets in Base 4

Best Known (83−39, 83, s)-Nets in Base 4

(83−39, 83, 66)-Net over F₄ — Constructive and digital

Digital (44, 83, 66)-net over F₄, using

1 times m-reduction [i] based on digital (44, 84, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 42, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(83−39, 83, 84)-Net over F₄ — Digital

Digital (44, 83, 84)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−39, 83, 1032)-Net in Base 4 — Upper bound on s

There is no (44, 83, 1033)-net in base 4, because

1 times m-reduction [i] would yield (44, 82, 1033)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 389420 608890 488057 120316 134587 880222 619468 098048 > 4⁸² [i]