MinT - Best Known (40, 74, s)-Nets in Base 4

Best Known (40, 74, s)-Nets in Base 4

(40, 74, 76)-Net over F₄ — Constructive and digital

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, 74, 83)-Net over F₄ — Digital

Digital (40, 74, 83)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 74, 985)-Net in Base 4 — Upper bound on s

There is no (40, 74, 986)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 360 578484 268758 433485 252403 633154 454630 049525 > 4⁷⁴ [i]