MinT - Best Known (249−109, 249, s)-Nets in Base 3

Best Known (249−109, 249, s)-Nets in Base 3

(249−109, 249, 128)-Net over F₃ — Constructive and digital

Digital (140, 249, 128)-net over F₃, using

t-expansion [i] based on digital (138, 249, 128)-net over F₃, using
- 1 times m-reduction [i] based on digital (138, 250, 128)-net over F₃, using
  - trace code for nets [i] based on digital (13, 125, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
        a function field by GarcÃa and Quoos [i]

(249−109, 249, 176)-Net over F₃ — Digital

Digital (140, 249, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−109, 249, 1575)-Net in Base 3 — Upper bound on s

There is no (140, 249, 1576)-net in base 3, because

1 times m-reduction [i] would yield (140, 248, 1576)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21521 575042 735027 140973 595538 998751 763322 057849 936806 788172 431586 945607 236078 652689 190387 546076 039769 262465 713045 673457 > 3²⁴⁸ [i]