MinT - Best Known (27, 27+25, s)-Nets in Base 4

Best Known (27, 27+25, s)-Nets in Base 4

(27, 27+25, 48)-Net over F₄ — Constructive and digital

Digital (27, 52, 48)-net over F₄, using

trace code for nets [i] based on digital (1, 26, 24)-net over F₁₆, using
- net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(27, 27+25, 56)-Net over F₄ — Digital

Digital (27, 52, 56)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 27+25, 628)-Net in Base 4 — Upper bound on s

There is no (27, 52, 629)-net in base 4, because

1 times m-reduction [i] would yield (27, 51, 629)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 088630 675221 334018 545480 078590 > 4⁵¹ [i]