MinT - Best Known (259−71, 259, s)-Nets in Base 4

Best Known (259−71, 259, s)-Nets in Base 4

(259−71, 259, 531)-Net over F₄ — Constructive and digital

Digital (188, 259, 531)-net over F₄, using

4¹ times duplication [i] based on digital (187, 258, 531)-net over F₄, using
- t-expansion [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(259−71, 259, 1525)-Net over F₄ — Digital

Digital (188, 259, 1525)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−71, 259, 127082)-Net in Base 4 — Upper bound on s

There is no (188, 259, 127083)-net in base 4, because

1 times m-reduction [i] would yield (188, 258, 127083)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214536 124241 015766 987157 375931 082186 545309 363728 772765 714548 430127 124879 641725 850593 224088 325378 279302 471636 608961 697629 818286 183873 568804 914384 323877 699020 > 4²⁵⁸ [i]