MinT - Best Known (120−45, 120, s)-Nets in Base 9

Best Known (120−45, 120, s)-Nets in Base 9

(120−45, 120, 448)-Net over F₉ — Constructive and digital

Digital (75, 120, 448)-net over F₉, using

4 times m-reduction [i] based on digital (75, 124, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 62, 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]

(120−45, 120, 886)-Net over F₉ — Digital

Digital (75, 120, 886)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−45, 120, 164177)-Net in Base 9 — Upper bound on s

There is no (75, 120, 164178)-net in base 9, because

1 times m-reduction [i] would yield (75, 119, 164178)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 358850 292805 854303 523098 629990 015854 912822 862007 016488 275788 755607 640422 696755 719501 076480 055643 288078 723705 258913 > 9¹¹⁹ [i]