MinT - Best Known (173−47, 173, s)-Nets in Base 4

Best Known (173−47, 173, s)-Nets in Base 4

(173−47, 173, 531)-Net over F₄ — Constructive and digital

Digital (126, 173, 531)-net over F₄, using

t-expansion [i] based on digital (125, 173, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (125, 177, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 59, 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]

(173−47, 173, 1125)-Net over F₄ — Digital

Digital (126, 173, 1125)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−47, 173, 99911)-Net in Base 4 — Upper bound on s

There is no (126, 173, 99912)-net in base 4, because

1 times m-reduction [i] would yield (126, 172, 99912)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 839863 284844 804083 512866 033858 209748 844358 258331 700779 245971 168146 085067 280041 498174 519340 918208 976308 > 4¹⁷² [i]