MinT - Best Known (210−65, 210, s)-Nets in Base 4

Best Known (210−65, 210, s)-Nets in Base 4

(210−65, 210, 450)-Net over F₄ — Constructive and digital

Digital (145, 210, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 105, 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]

(210−65, 210, 762)-Net over F₄ — Digital

Digital (145, 210, 762)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−65, 210, 36446)-Net in Base 4 — Upper bound on s

There is no (145, 210, 36447)-net in base 4, because

1 times m-reduction [i] would yield (145, 209, 36447)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677418 003793 594485 987408 028148 685394 378066 745559 775816 435609 281919 421828 136281 663728 717008 271800 416987 615466 464818 194077 462650 > 4²⁰⁹ [i]