MinT - Best Known (55, 55+31, s)-Nets in Base 4

Best Known (55, 55+31, s)-Nets in Base 4

(55, 55+31, 130)-Net over F₄ — Constructive and digital

Digital (55, 86, 130)-net over F₄, using

12 times m-reduction [i] based on digital (55, 98, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 49, 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]

(55, 55+31, 208)-Net over F₄ — Digital

Digital (55, 86, 208)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+31, 5512)-Net in Base 4 — Upper bound on s

There is no (55, 86, 5513)-net in base 4, because

1 times m-reduction [i] would yield (55, 85, 5513)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1497 240296 489641 828696 390942 003750 640260 479879 894400 > 4⁸⁵ [i]