MinT - Best Known (247−92, 247, s)-Nets in Base 4

Best Known (247−92, 247, s)-Nets in Base 4

(247−92, 247, 160)-Net over F₄ — Constructive and digital

Digital (155, 247, 160)-net over F₄, using

6 times m-reduction [i] based on digital (155, 253, 160)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (33, 82, 56)-net over F₄, using
    - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
        F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 171, 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]

(247−92, 247, 448)-Net over F₄ — Digital

Digital (155, 247, 448)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−92, 247, 10216)-Net in Base 4 — Upper bound on s

There is no (155, 247, 10217)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51241 283298 208810 331948 804862 281560 981871 150405 436907 995020 042835 240496 147941 905439 267041 037673 445302 574697 428321 953782 463591 692329 884142 235258 493024 > 4²⁴⁷ [i]