MinT - Best Known (51, 51+43, s)-Nets in Base 4

Best Known (51, 51+43, s)-Nets in Base 4

(51, 51+43, 90)-Net over F₄ — Constructive and digital

Digital (51, 94, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 47, 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]

(51, 51+43, 101)-Net over F₄ — Digital

Digital (51, 94, 101)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+43, 1324)-Net in Base 4 — Upper bound on s

There is no (51, 94, 1325)-net in base 4, because

1 times m-reduction [i] would yield (51, 93, 1325)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 98 501627 696777 450890 683467 947508 562002 292232 427223 880936 > 4⁹³ [i]