MinT - Best Known (146−44, 146, s)-Nets in Base 9

Best Known (146−44, 146, s)-Nets in Base 9

(146−44, 146, 770)-Net over F₉ — Constructive and digital

Digital (102, 146, 770)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 26, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]
2. digital (76, 120, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 60, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(146−44, 146, 3689)-Net over F₉ — Digital

Digital (102, 146, 3689)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−44, 146, 2434786)-Net in Base 9 — Upper bound on s

There is no (102, 146, 2434787)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 864431 224897 424682 387839 849392 767808 346420 952471 137898 844838 370252 173033 714231 853623 851831 192140 478937 096724 195414 969076 911247 553595 855505 > 9¹⁴⁶ [i]