MinT - Best Known (107, 156, s)-Nets in Base 3

Best Known (107, 156, s)-Nets in Base 3

(107, 156, 156)-Net over F₃ — Constructive and digital

Digital (107, 156, 156)-net over F₃, using

14 times m-reduction [i] based on digital (107, 170, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 85, 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]

(107, 156, 310)-Net over F₃ — Digital

Digital (107, 156, 310)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 156, 5888)-Net in Base 3 — Upper bound on s

There is no (107, 156, 5889)-net in base 3, because

1 times m-reduction [i] would yield (107, 155, 5889)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 043673 463715 718533 787520 896097 896332 436551 700074 981658 979230 447575 775457 > 3¹⁵⁵ [i]