MinT - Best Known (41, 134, s)-Nets in Base 9

Best Known (41, 134, s)-Nets in Base 9

(41, 134, 81)-Net over F₉ — Constructive and digital

Digital (41, 134, 81)-net over F₉, using

t-expansion [i] based on digital (32, 134, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(41, 134, 140)-Net over F₉ — Digital

Digital (41, 134, 140)-net over F₉, using

t-expansion [i] based on digital (39, 134, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(41, 134, 1263)-Net in Base 9 — Upper bound on s

There is no (41, 134, 1264)-net in base 9, because

1 times m-reduction [i] would yield (41, 133, 1264)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 331798 768681 004875 182776 851130 283463 478526 460277 245555 808069 119656 289730 068006 724476 632436 946372 803192 104548 373931 392898 204417 > 9¹³³ [i]