MinT - Best Known (61−29, 61, s)-Nets in Base 4

Best Known (61−29, 61, s)-Nets in Base 4

(61−29, 61, 48)-Net over F₄ — Constructive and digital

Digital (32, 61, 48)-net over F₄, using

1 times m-reduction [i] based on digital (32, 62, 48)-net over F₄, using
- trace code for nets [i] based on digital (1, 31, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]

(61−29, 61, 65)-Net over F₄ — Digital

Digital (32, 61, 65)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61−29, 61, 755)-Net in Base 4 — Upper bound on s

There is no (32, 61, 756)-net in base 4, because

1 times m-reduction [i] would yield (32, 60, 756)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 340439 205641 527060 923869 121150 149220 > 4⁶⁰ [i]