MinT - Best Known (50, 50+95, s)-Nets in Base 9

Best Known (50, 50+95, s)-Nets in Base 9

(50, 50+95, 81)-Net over F₉ — Constructive and digital

Digital (50, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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]

(50, 50+95, 182)-Net over F₉ — Digital

Digital (50, 145, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(50, 50+95, 1897)-Net in Base 9 — Upper bound on s

There is no (50, 145, 1898)-net in base 9, because

1 times m-reduction [i] would yield (50, 144, 1898)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 262630 224012 522731 365124 229513 881084 965425 595475 980006 771350 909880 072198 385982 194145 451299 477534 306099 148962 157236 539348 253549 118846 576497 > 9¹⁴⁴ [i]