MinT - Best Known (43−17, 43, s)-Nets in Base 4

Best Known (43−17, 43, s)-Nets in Base 4

(43−17, 43, 90)-Net over F₄ — Constructive and digital

Digital (26, 43, 90)-net over F₄, using

1 times m-reduction [i] based on digital (26, 44, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 22, 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]

(43−17, 43, 95)-Net over F₄ — Digital

Digital (26, 43, 95)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(43−17, 43, 1810)-Net in Base 4 — Upper bound on s

There is no (26, 43, 1811)-net in base 4, because

1 times m-reduction [i] would yield (26, 42, 1811)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19 346026 405559 874313 772110 > 4⁴² [i]