MinT - Best Known (196−101, 196, s)-Nets in Base 4

Best Known (196−101, 196, s)-Nets in Base 4

(196−101, 196, 104)-Net over F₄ — Constructive and digital

Digital (95, 196, 104)-net over F₄, using

t-expansion [i] based on digital (73, 196, 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]

(196−101, 196, 144)-Net over F₄ — Digital

Digital (95, 196, 144)-net over F₄, using

t-expansion [i] based on digital (91, 196, 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]

(196−101, 196, 1406)-Net in Base 4 — Upper bound on s

There is no (95, 196, 1407)-net in base 4, because

1 times m-reduction [i] would yield (95, 195, 1407)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2554 452552 008369 539315 846050 021438 036119 764505 663934 943855 472408 711956 864045 204466 403497 993944 968927 930969 826412 457175 > 4¹⁹⁵ [i]