MinT - Best Known (210−63, 210, s)-Nets in Base 4

Best Known (210−63, 210, s)-Nets in Base 4

(210−63, 210, 531)-Net over F₄ — Constructive and digital

Digital (147, 210, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(210−63, 210, 865)-Net over F₄ — Digital

Digital (147, 210, 865)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−63, 210, 47394)-Net in Base 4 — Upper bound on s

There is no (147, 210, 47395)-net in base 4, because

1 times m-reduction [i] would yield (147, 209, 47395)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677077 414626 390567 554255 988387 176490 427690 167719 467879 646862 999619 535302 376972 158905 125334 414711 437357 552022 413400 292876 028032 > 4²⁰⁹ [i]