MinT - Best Known (254−81, 254, s)-Nets in Base 4

Best Known (254−81, 254, s)-Nets in Base 4

(254−81, 254, 450)-Net over F₄ — Constructive and digital

Digital (173, 254, 450)-net over F₄, using

t-expansion [i] based on digital (170, 254, 450)-net over F₄, using
- 6 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
  - trace code for nets [i] based on digital (40, 130, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(254−81, 254, 801)-Net over F₄ — Digital

Digital (173, 254, 801)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−81, 254, 33750)-Net in Base 4 — Upper bound on s

There is no (173, 254, 33751)-net in base 4, because

1 times m-reduction [i] would yield (173, 253, 33751)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 679450 444861 780300 088225 230815 959730 319117 571335 915773 686315 739309 885195 158725 023535 893013 443431 374769 302589 718074 048162 940474 692514 857075 596292 729876 > 4²⁵³ [i]