MinT - Best Known (90, 90+151, s)-Nets in Base 4

Best Known (90, 90+151, s)-Nets in Base 4

(90, 90+151, 104)-Net over F₄ — Constructive and digital

Digital (90, 241, 104)-net over F₄, using

t-expansion [i] based on digital (73, 241, 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]

(90, 90+151, 129)-Net over F₄ — Digital

Digital (90, 241, 129)-net over F₄, using

t-expansion [i] based on digital (81, 241, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(90, 90+151, 748)-Net in Base 4 — Upper bound on s

There is no (90, 241, 749)-net in base 4, because

1 times m-reduction [i] would yield (90, 240, 749)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 133209 883772 328420 729279 926888 169211 843976 216167 401804 622947 307805 261287 665916 521734 759911 339696 425152 534903 390148 981589 656517 540979 749490 027596 > 4²⁴⁰ [i]