MinT - Best Known (190−116, 190, s)-Nets in Base 4

Best Known (190−116, 190, s)-Nets in Base 4

(190−116, 190, 104)-Net over F₄ — Constructive and digital

Digital (74, 190, 104)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(190−116, 190, 112)-Net over F₄ — Digital

Digital (74, 190, 112)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(190−116, 190, 655)-Net in Base 4 — Upper bound on s

There is no (74, 190, 656)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 582694 970435 050299 484490 574639 734776 159479 457438 141199 700968 405704 017674 966017 126924 438733 679492 249951 861090 785480 > 4¹⁹⁰ [i]