MinT - Best Known (90−30, 90, s)-Nets in Base 4

Best Known (90−30, 90, s)-Nets in Base 4

(90−30, 90, 195)-Net over F₄ — Constructive and digital

Digital (60, 90, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 30, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(90−30, 90, 290)-Net over F₄ — Digital

Digital (60, 90, 290)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−30, 90, 8758)-Net in Base 4 — Upper bound on s

There is no (60, 90, 8759)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 534797 686903 379665 620986 358613 310234 902947 304194 357048 > 4⁹⁰ [i]