MinT - Best Known (246−95, 246, s)-Nets in Base 3

Best Known (246−95, 246, s)-Nets in Base 3

(246−95, 246, 156)-Net over F₃ — Constructive and digital

Digital (151, 246, 156)-net over F₃, using

t-expansion [i] based on digital (147, 246, 156)-net over F₃, using
- 4 times m-reduction [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]

(246−95, 246, 247)-Net over F₃ — Digital

Digital (151, 246, 247)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−95, 246, 2773)-Net in Base 3 — Upper bound on s

There is no (151, 246, 2774)-net in base 3, because

1 times m-reduction [i] would yield (151, 245, 2774)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 792 089413 264035 186725 198655 868595 456786 087567 031307 571313 389679 832796 864467 922707 256646 770681 908632 377390 577176 373321 > 3²⁴⁵ [i]