MinT - Best Known (90−40, 90, s)-Nets in Base 4

Best Known (90−40, 90, s)-Nets in Base 4

(90−40, 90, 98)-Net over F₄ — Constructive and digital

Digital (50, 90, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 45, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(90−40, 90, 107)-Net over F₄ — Digital

Digital (50, 90, 107)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−40, 90, 1401)-Net in Base 4 — Upper bound on s

There is no (50, 90, 1402)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 550286 483137 446740 966636 665380 754677 329940 052025 881446 > 4⁹⁰ [i]