MinT - Best Known (145−40, 145, s)-Nets in Base 4

Best Known (145−40, 145, s)-Nets in Base 4

(145−40, 145, 531)-Net over F₄ — Constructive and digital

Digital (105, 145, 531)-net over F₄, using

2 times m-reduction [i] based on digital (105, 147, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 49, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(145−40, 145, 908)-Net over F₄ — Digital

Digital (105, 145, 908)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−40, 145, 64122)-Net in Base 4 — Upper bound on s

There is no (105, 145, 64123)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 603446 638798 821313 921749 776437 828272 775512 077372 147344 180945 880407 326710 549876 726266 > 4¹⁴⁵ [i]