MinT - Best Known (196−57, 196, s)-Nets in Base 4

Best Known (196−57, 196, s)-Nets in Base 4

(196−57, 196, 531)-Net over F₄ — Constructive and digital

Digital (139, 196, 531)-net over F₄, using

2 times m-reduction [i] based on digital (139, 198, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 66, 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]

(196−57, 196, 930)-Net over F₄ — Digital

Digital (139, 196, 930)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−57, 196, 58699)-Net in Base 4 — Upper bound on s

There is no (139, 196, 58700)-net in base 4, because

1 times m-reduction [i] would yield (139, 195, 58700)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2522 607327 766774 199109 300438 542434 224074 891741 080316 853451 414162 194115 520205 341216 698400 829830 502547 646953 799444 197840 > 4¹⁹⁵ [i]