MinT - Best Known (185−105, 185, s)-Nets in Base 4

Best Known (185−105, 185, s)-Nets in Base 4

(185−105, 185, 104)-Net over F₄ — Constructive and digital

Digital (80, 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]

(185−105, 185, 112)-Net over F₄ — Digital

Digital (80, 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]

(185−105, 185, 868)-Net in Base 4 — Upper bound on s

There is no (80, 185, 869)-net in base 4, because

1 times m-reduction [i] would yield (80, 184, 869)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 631 885936 129431 492013 679308 081938 453543 779226 713079 258073 890459 900005 559921 509624 325980 430558 264763 545558 375100 > 4¹⁸⁴ [i]