MinT - Best Known (56−23, 56, s)-Nets in Base 4

Best Known (56−23, 56, s)-Nets in Base 4

(56−23, 56, 98)-Net over F₄ — Constructive and digital

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]

(56−23, 56, 1667)-Net in Base 4 — Upper bound on s

There is no (33, 56, 1668)-net in base 4, because

1 times m-reduction [i] would yield (33, 55, 1668)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1306 297824 707395 113609 115138 376080 > 4⁵⁵ [i]