MinT - Best Known (243−71, 243, s)-Nets in Base 4

Best Known (243−71, 243, s)-Nets in Base 4

(243−71, 243, 531)-Net over F₄ — Constructive and digital

Digital (172, 243, 531)-net over F₄, using

t-expansion [i] based on digital (171, 243, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (171, 246, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 82, 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]

(243−71, 243, 1094)-Net over F₄ — Digital

Digital (172, 243, 1094)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−71, 243, 67417)-Net in Base 4 — Upper bound on s

There is no (172, 243, 67418)-net in base 4, because

1 times m-reduction [i] would yield (172, 242, 67418)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 960571 298885 362174 375662 028288 167693 371426 088659 859659 213569 543680 585223 570719 430120 113197 093073 334109 386923 720481 770568 521055 728221 161101 993480 > 4²⁴² [i]