MinT - Best Known (23−11, 23, s)-Nets in Base 4

Best Known (23−11, 23, s)-Nets in Base 4

(23−11, 23, 34)-Net over F₄ — Constructive and digital

Digital (12, 23, 34)-net over F₄, using

1 times m-reduction [i] based on digital (12, 24, 34)-net over F₄, using
- trace code for nets [i] based on digital (0, 12, 17)-net over F₁₆, using
  - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
      - the rational function field F₁₆(x) [i]
    - Niederreiter sequence [i]

(23−11, 23, 37)-Net over F₄ — Digital

Digital (12, 23, 37)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(23−11, 23, 383)-Net in Base 4 — Upper bound on s

There is no (12, 23, 384)-net in base 4, because

1 times m-reduction [i] would yield (12, 22, 384)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 17 727150 478177 > 4²² [i]