MinT - Best Known (75−33, 75, s)-Nets in Base 4

Best Known (75−33, 75, s)-Nets in Base 4

(75−33, 75, 90)-Net over F₄ — Constructive and digital

Digital (42, 75, 90)-net over F₄, using

1 times m-reduction [i] based on digital (42, 76, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 38, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(75−33, 75, 97)-Net over F₄ — Digital

Digital (42, 75, 97)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−33, 75, 1367)-Net in Base 4 — Upper bound on s

There is no (42, 75, 1368)-net in base 4, because

1 times m-reduction [i] would yield (42, 74, 1368)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 359 210205 180944 245695 993208 854268 091424 063985 > 4⁷⁴ [i]