MinT - Best Known (40, 40+35, s)-Nets in Base 4

Best Known (40, 40+35, s)-Nets in Base 4

(40, 40+35, 66)-Net over F₄ — Constructive and digital

Digital (40, 75, 66)-net over F₄, using

1 times m-reduction [i] based on digital (40, 76, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 38, 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]

(40, 40+35, 80)-Net over F₄ — Digital

Digital (40, 75, 80)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+35, 985)-Net in Base 4 — Upper bound on s

There is no (40, 75, 986)-net in base 4, because

1 times m-reduction [i] would yield (40, 74, 986)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 360 578484 268758 433485 252403 633154 454630 049525 > 4⁷⁴ [i]