MinT - Best Known (90−39, 90, s)-Nets in Base 4

Best Known (90−39, 90, s)-Nets in Base 4

(90−39, 90, 130)-Net over F₄ — Constructive and digital

Digital (51, 90, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 45, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(90−39, 90, 1731)-Net in Base 4 — Upper bound on s

There is no (51, 90, 1732)-net in base 4, because

1 times m-reduction [i] would yield (51, 89, 1732)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 384683 754212 657508 087485 414979 160565 865992 750929 090732 > 4⁸⁹ [i]