MinT - Best Known (168−95, 168, s)-Nets in Base 4

Best Known (168−95, 168, s)-Nets in Base 4

(168−95, 168, 104)-Net over F₄ — Constructive and digital

Digital (73, 168, 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]

(168−95, 168, 112)-Net over F₄ — Digital

Digital (73, 168, 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]

(168−95, 168, 805)-Net in Base 4 — Upper bound on s

There is no (73, 168, 806)-net in base 4, because

1 times m-reduction [i] would yield (73, 167, 806)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35500 712794 151483 850152 297592 024037 655297 577978 542003 964939 995176 090125 278410 714292 438501 299778 780800 > 4¹⁶⁷ [i]