MinT - Best Known (237−163, 237, s)-Nets in Base 4

Best Known (237−163, 237, s)-Nets in Base 4

(237−163, 237, 104)-Net over F₄ — Constructive and digital

Digital (74, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(237−163, 237, 112)-Net over F₄ — Digital

Digital (74, 237, 112)-net over F₄, using

t-expansion [i] based on digital (73, 237, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(237−163, 237, 521)-Net in Base 4 — Upper bound on s

There is no (74, 237, 522)-net in base 4, because

1 times m-reduction [i] would yield (74, 236, 522)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12528 960039 205630 443865 472412 394972 734308 420528 166288 376538 968556 599849 676829 733757 988166 998158 010918 311707 893478 387373 136393 493221 440558 983648 > 4²³⁶ [i]