MinT - Best Known (19−9, 19, s)-Nets in Base 4

Best Known (19−9, 19, s)-Nets in Base 4

(19−9, 19, 34)-Net over F₄ — Constructive and digital

Digital (10, 19, 34)-net over F₄, using

1 times m-reduction [i] based on digital (10, 20, 34)-net over F₄, using
- trace code for nets [i] based on digital (0, 10, 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]

(19−9, 19, 36)-Net over F₄ — Digital

Digital (10, 19, 36)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(19−9, 19, 374)-Net in Base 4 — Upper bound on s

There is no (10, 19, 375)-net in base 4, because

1 times m-reduction [i] would yield (10, 18, 375)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 68775 680251 > 4¹⁸ [i]