MinT - Best Known (55−22, 55, s)-Nets in Base 4

Best Known (55−22, 55, s)-Nets in Base 4

(55−22, 55, 98)-Net over F₄ — Constructive and digital

Digital (33, 55, 98)-net over F₄, using

1 times m-reduction [i] based on digital (33, 56, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 28, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(55−22, 55, 106)-Net over F₄ — Digital

Digital (33, 55, 106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−22, 55, 1667)-Net in Base 4 — Upper bound on s

There is no (33, 55, 1668)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1306 297824 707395 113609 115138 376080 > 4⁵⁵ [i]