MinT - Best Known (85, 85+47, s)-Nets in Base 9

Best Known (85, 85+47, s)-Nets in Base 9

(85, 85+47, 740)-Net over F₉ — Constructive and digital

Digital (85, 132, 740)-net over F₉, using

6 times m-reduction [i] based on digital (85, 138, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 69, 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]

(85, 85+47, 1254)-Net over F₉ — Digital

Digital (85, 132, 1254)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+47, 320908)-Net in Base 9 — Upper bound on s

There is no (85, 132, 320909)-net in base 9, because

1 times m-reduction [i] would yield (85, 131, 320909)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101342 303886 339889 530812 391190 813601 256937 112829 371281 921271 667492 048225 405968 396542 885134 210426 462508 757745 349406 745006 695193 > 9¹³¹ [i]