MinT - Best Known (43−19, 43, s)-Nets in Base 4

Best Known (43−19, 43, s)-Nets in Base 4

(43−19, 43, 66)-Net over F₄ — Constructive and digital

Digital (24, 43, 66)-net over F₄, using

1 times m-reduction [i] based on digital (24, 44, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 22, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(43−19, 43, 884)-Net in Base 4 — Upper bound on s

There is no (24, 43, 885)-net in base 4, because

1 times m-reduction [i] would yield (24, 42, 885)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19 387299 181254 752050 166512 > 4⁴² [i]