MinT - Best Known (54, 54+45, s)-Nets in Base 4

Best Known (54, 54+45, s)-Nets in Base 4

(54, 54+45, 90)-Net over F₄ — Constructive and digital

Digital (54, 99, 90)-net over F₄, using

1 times m-reduction [i] based on digital (54, 100, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 50, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(54, 54+45, 108)-Net over F₄ — Digital

Digital (54, 99, 108)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+45, 1433)-Net in Base 4 — Upper bound on s

There is no (54, 99, 1434)-net in base 4, because

1 times m-reduction [i] would yield (54, 98, 1434)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 101745 844407 921018 373275 333525 030042 817646 222528 414570 227180 > 4⁹⁸ [i]