MinT - Best Known (44−19, 44, s)-Nets in Base 4

Best Known (44−19, 44, s)-Nets in Base 4

(44−19, 44, 76)-Net over F₄ — Constructive and digital

Digital (25, 44, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 22, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(44−19, 44, 1033)-Net in Base 4 — Upper bound on s

There is no (25, 44, 1034)-net in base 4, because

1 times m-reduction [i] would yield (25, 43, 1034)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 77 860162 501006 764379 416103 > 4⁴³ [i]