MinT - Best Known (85, 85+57, s)-Nets in Base 9

Best Known (85, 85+57, s)-Nets in Base 9

(85, 85+57, 448)-Net over F₉ — Constructive and digital

Digital (85, 142, 448)-net over F₉, using

2 times m-reduction [i] based on digital (85, 144, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 72, 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]

(85, 85+57, 717)-Net over F₉ — Digital

Digital (85, 142, 717)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+57, 90183)-Net in Base 9 — Upper bound on s

There is no (85, 142, 90184)-net in base 9, because

1 times m-reduction [i] would yield (85, 141, 90184)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 424416 738369 437346 413715 052699 406869 211164 485120 095630 120095 251637 567037 849208 168374 930971 803647 781248 103944 563575 643684 053403 793665 > 9¹⁴¹ [i]