MinT - Best Known (39−17, 39, s)-Nets in Base 4

Best Known (39−17, 39, s)-Nets in Base 4

(39−17, 39, 66)-Net over F₄ — Constructive and digital

Digital (22, 39, 66)-net over F₄, using

1 times m-reduction [i] based on digital (22, 40, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 20, 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]

(39−17, 39, 902)-Net in Base 4 — Upper bound on s

There is no (22, 39, 903)-net in base 4, because

1 times m-reduction [i] would yield (22, 38, 903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 75951 157824 441136 304560 > 4³⁸ [i]