MinT - Best Known (250−90, 250, s)-Nets in Base 3

Best Known (250−90, 250, s)-Nets in Base 3

(250−90, 250, 162)-Net over F₃ — Constructive and digital

Digital (160, 250, 162)-net over F₃, using

t-expansion [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(250−90, 250, 308)-Net over F₃ — Digital

Digital (160, 250, 308)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−90, 250, 3898)-Net in Base 3 — Upper bound on s

There is no (160, 250, 3899)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191508 704167 290853 921634 858112 666177 564828 748088 203957 269671 330913 006923 918694 453124 872211 115950 745036 620305 687660 142623 > 3²⁵⁰ [i]