MinT - Best Known (163, 163+77, s)-Nets in Base 4

Best Known (163, 163+77, s)-Nets in Base 4

(163, 163+77, 450)-Net over F₄ — Constructive and digital

Digital (163, 240, 450)-net over F₄, using

6 times m-reduction [i] based on digital (163, 246, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 123, 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]

(163, 163+77, 744)-Net over F₄ — Digital

Digital (163, 240, 744)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+77, 30611)-Net in Base 4 — Upper bound on s

There is no (163, 240, 30612)-net in base 4, because

1 times m-reduction [i] would yield (163, 239, 30612)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 781194 380301 276004 140961 556644 669162 606843 576648 350963 544902 728016 051794 211814 840840 388406 421221 864615 647349 284348 173648 072515 215418 532573 551664 > 4²³⁹ [i]