MinT - Best Known (79, 79+51, s)-Nets in Base 9

Best Known (79, 79+51, s)-Nets in Base 9

(79, 79+51, 448)-Net over F₉ — Constructive and digital

Digital (79, 130, 448)-net over F₉, using

2 times m-reduction [i] based on digital (79, 132, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 66, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(79, 79+51, 751)-Net over F₉ — Digital

Digital (79, 130, 751)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+51, 106749)-Net in Base 9 — Upper bound on s

There is no (79, 130, 106750)-net in base 9, because

1 times m-reduction [i] would yield (79, 129, 106750)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 236061 758199 792365 703173 228845 253802 673918 671819 603937 144524 766966 086285 150622 538553 143461 623480 311030 391963 312034 517361 > 9¹²⁹ [i]