MinT - Best Known (90−42, 90, s)-Nets in Base 4

Best Known (90−42, 90, s)-Nets in Base 4

(90−42, 90, 76)-Net over F₄ — Constructive and digital

Digital (48, 90, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 45, 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]

(90−42, 90, 92)-Net over F₄ — Digital

Digital (48, 90, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−42, 90, 1083)-Net in Base 4 — Upper bound on s

There is no (48, 90, 1084)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 541354 445480 746444 470619 554084 649997 741041 421816 729922 > 4⁹⁰ [i]