MinT - Best Known (154, 249, s)-Nets in Base 3

Best Known (154, 249, s)-Nets in Base 3

(154, 249, 156)-Net over F₃ — Constructive and digital

Digital (154, 249, 156)-net over F₃, using

t-expansion [i] based on digital (147, 249, 156)-net over F₃, using
- 1 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]

(154, 249, 259)-Net over F₃ — Digital

Digital (154, 249, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 249, 2978)-Net in Base 3 — Upper bound on s

There is no (154, 249, 2979)-net in base 3, because

1 times m-reduction [i] would yield (154, 248, 2979)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21439 415958 080668 719767 200873 799387 046818 146115 389535 926348 154246 735335 487571 747677 081401 056753 019814 577674 783525 151027 > 3²⁴⁸ [i]