MinT - Best Known (245−149, 245, s)-Nets in Base 4

Best Known (245−149, 245, s)-Nets in Base 4

(245−149, 245, 104)-Net over F₄ — Constructive and digital

Digital (96, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(245−149, 245, 144)-Net over F₄ — Digital

Digital (96, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(245−149, 245, 854)-Net in Base 4 — Upper bound on s

There is no (96, 245, 855)-net in base 4, because

1 times m-reduction [i] would yield (96, 244, 855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 832 903931 303069 165682 557780 839637 734756 982261 035612 712357 294543 587410 961972 381703 000544 402838 882934 365992 692603 693746 593507 677041 829691 005613 874966 > 4²⁴⁴ [i]