MinT - Best Known (185−109, 185, s)-Nets in Base 4

Best Known (185−109, 185, s)-Nets in Base 4

(185−109, 185, 104)-Net over F₄ — Constructive and digital

Digital (76, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(185−109, 185, 112)-Net over F₄ — Digital

Digital (76, 185, 112)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(185−109, 185, 743)-Net in Base 4 — Upper bound on s

There is no (76, 185, 744)-net in base 4, because

1 times m-reduction [i] would yield (76, 184, 744)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 632 026832 189382 950924 400418 102956 944129 068912 051386 199118 707741 018819 676253 234024 842793 679517 224287 284654 805484 > 4¹⁸⁴ [i]