MinT - Best Known (238−71, 238, s)-Nets in Base 4

Best Known (238−71, 238, s)-Nets in Base 4

(238−71, 238, 531)-Net over F₄ — Constructive and digital

Digital (167, 238, 531)-net over F₄, using

2 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]

(238−71, 238, 985)-Net over F₄ — Digital

Digital (167, 238, 985)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−71, 238, 55299)-Net in Base 4 — Upper bound on s

There is no (167, 238, 55300)-net in base 4, because

1 times m-reduction [i] would yield (167, 237, 55300)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48782 815222 424523 489952 206631 284710 389828 812714 780504 504876 408066 451332 079920 196909 288652 195354 120213 471440 540054 953898 075559 681192 474004 651712 > 4²³⁷ [i]