MinT - Best Known (169−95, 169, s)-Nets in Base 4

Best Known (169−95, 169, s)-Nets in Base 4

(169−95, 169, 104)-Net over F₄ — Constructive and digital

Digital (74, 169, 104)-net over F₄, using

t-expansion [i] based on digital (73, 169, 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]

(169−95, 169, 112)-Net over F₄ — Digital

Digital (74, 169, 112)-net over F₄, using

t-expansion [i] based on digital (73, 169, 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]

(169−95, 169, 830)-Net in Base 4 — Upper bound on s

There is no (74, 169, 831)-net in base 4, because

1 times m-reduction [i] would yield (74, 168, 831)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140121 870529 265748 283736 099475 107762 002899 245048 659068 103752 352018 632212 501467 959506 663370 128573 069212 > 4¹⁶⁸ [i]