MinT - Best Known (40, 40+33, s)-Nets in Base 4

Best Known (40, 40+33, s)-Nets in Base 4

(40, 40+33, 76)-Net over F₄ — Constructive and digital

Digital (40, 73, 76)-net over F₄, using

1 times m-reduction [i] based on digital (40, 74, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 37, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(40, 40+33, 87)-Net over F₄ — Digital

Digital (40, 73, 87)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+33, 1147)-Net in Base 4 — Upper bound on s

There is no (40, 73, 1148)-net in base 4, because

1 times m-reduction [i] would yield (40, 72, 1148)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 22 351691 829515 086809 241648 215875 053546 101685 > 4⁷² [i]