MinT - Best Known (149−70, 149, s)-Nets in Base 9

Best Known (149−70, 149, s)-Nets in Base 9

(149−70, 149, 300)-Net over F₉ — Constructive and digital

Digital (79, 149, 300)-net over F₉, using

1 times m-reduction [i] based on digital (79, 150, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 75, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(149−70, 149, 360)-Net over F₉ — Digital

Digital (79, 149, 360)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−70, 149, 20047)-Net in Base 9 — Upper bound on s

There is no (79, 149, 20048)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15226 374001 389359 350973 928133 319384 688892 746698 980072 126269 191645 088945 102309 428987 271662 654928 926174 772109 903779 222997 525751 102539 638821 184897 > 9¹⁴⁹ [i]