MinT - Best Known (233−65, 233, s)-Nets in Base 4

Best Known (233−65, 233, s)-Nets in Base 4

(233−65, 233, 531)-Net over F₄ — Constructive and digital

Digital (168, 233, 531)-net over F₄, using

t-expansion [i] based on digital (167, 233, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 80, 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]

(233−65, 233, 1289)-Net over F₄ — Digital

Digital (168, 233, 1289)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−65, 233, 98759)-Net in Base 4 — Upper bound on s

There is no (168, 233, 98760)-net in base 4, because

1 times m-reduction [i] would yield (168, 232, 98760)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 641375 629433 356885 157952 537326 707296 558699 433431 846047 826791 041834 211067 348418 257052 955627 931179 714342 455250 772073 867501 210172 829588 515978 > 4²³² [i]