MinT - Best Known (241−129, 241, s)-Nets in Base 4

Best Known (241−129, 241, s)-Nets in Base 4

(241−129, 241, 130)-Net over F₄ — Constructive and digital

Digital (112, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(241−129, 241, 165)-Net over F₄ — Digital

Digital (112, 241, 165)-net over F₄, using

t-expansion [i] based on digital (109, 241, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(241−129, 241, 1436)-Net in Base 4 — Upper bound on s

There is no (112, 241, 1437)-net in base 4, because

1 times m-reduction [i] would yield (112, 240, 1437)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 162571 095917 618104 741117 133325 589154 598502 020022 237844 281881 157841 782639 408912 654177 034345 348402 363124 974647 438936 589197 928328 245703 871177 153306 > 4²⁴⁰ [i]