MinT - Best Known (90−28, 90, s)-Nets in Base 4

Best Known (90−28, 90, s)-Nets in Base 4

(90−28, 90, 240)-Net over F₄ — Constructive and digital

Digital (62, 90, 240)-net over F₄, using

t-expansion [i] based on digital (61, 90, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 30, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(90−28, 90, 383)-Net over F₄ — Digital

Digital (62, 90, 383)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−28, 90, 14941)-Net in Base 4 — Upper bound on s

There is no (62, 90, 14942)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 533035 913880 298851 942824 071355 709682 223551 025815 469520 > 4⁹⁰ [i]