MinT - Best Known (148, 148+99, s)-Nets in Base 3

Best Known (148, 148+99, s)-Nets in Base 3

(148, 148+99, 156)-Net over F₃ — Constructive and digital

Digital (148, 247, 156)-net over F₃, using

t-expansion [i] based on digital (147, 247, 156)-net over F₃, using
- 3 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]

(148, 148+99, 224)-Net over F₃ — Digital

Digital (148, 247, 224)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+99, 2326)-Net in Base 3 — Upper bound on s

There is no (148, 247, 2327)-net in base 3, because

1 times m-reduction [i] would yield (148, 246, 2327)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2369 738627 616945 642578 486853 879963 774815 026551 603505 020891 293337 490078 268409 334244 153692 747173 293012 378611 887953 923023 > 3²⁴⁶ [i]