MinT - Best Known (211−61, 211, s)-Nets in Base 4

Best Known (211−61, 211, s)-Nets in Base 4

(211−61, 211, 531)-Net over F₄ — Constructive and digital

Digital (150, 211, 531)-net over F₄, using

t-expansion [i] based on digital (149, 211, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 71, 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]

(211−61, 211, 1015)-Net over F₄ — Digital

Digital (150, 211, 1015)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−61, 211, 65754)-Net in Base 4 — Upper bound on s

There is no (150, 211, 65755)-net in base 4, because

1 times m-reduction [i] would yield (150, 210, 65755)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 708282 181990 965683 608996 987459 417987 367727 962099 250274 945467 575961 324013 052674 016242 118800 452022 107987 778170 662723 781917 512016 > 4²¹⁰ [i]