MinT - Best Known (250−94, 250, s)-Nets in Base 3

Best Known (250−94, 250, s)-Nets in Base 3

(250−94, 250, 156)-Net over F₃ — Constructive and digital

Digital (156, 250, 156)-net over F₃, using

t-expansion [i] based on digital (147, 250, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 125, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(250−94, 250, 271)-Net over F₃ — Digital

Digital (156, 250, 271)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−94, 250, 3122)-Net in Base 3 — Upper bound on s

There is no (156, 250, 3123)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190760 573452 394478 360383 771538 172707 514727 253658 439396 136492 139367 004383 192248 261821 240024 706407 399947 935483 402198 038387 > 3²⁵⁰ [i]