MinT - Best Known (141−107, 141, s)-Nets in Base 9

Best Known (141−107, 141, s)-Nets in Base 9

(141−107, 141, 81)-Net over F₉ — Constructive and digital

Digital (34, 141, 81)-net over F₉, using

t-expansion [i] based on digital (32, 141, 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]

(141−107, 141, 128)-Net over F₉ — Digital

Digital (34, 141, 128)-net over F₉, using

t-expansion [i] based on digital (33, 141, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(141−107, 141, 821)-Net in Base 9 — Upper bound on s

There is no (34, 141, 822)-net in base 9, because

1 times m-reduction [i] would yield (34, 140, 822)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 485381 362353 627056 631015 194881 781568 081539 493633 868609 071340 092559 584774 622124 668709 634224 439686 030854 172662 354296 060043 708595 154929 > 9¹⁴⁰ [i]