MinT - Best Known (49, 49+83, s)-Nets in Base 9

Best Known (49, 49+83, s)-Nets in Base 9

(49, 49+83, 81)-Net over F₉ — Constructive and digital

Digital (49, 132, 81)-net over F₉, using

t-expansion [i] based on digital (32, 132, 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]

(49, 49+83, 168)-Net over F₉ — Digital

Digital (49, 132, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(49, 49+83, 2233)-Net in Base 9 — Upper bound on s

There is no (49, 132, 2234)-net in base 9, because

1 times m-reduction [i] would yield (49, 131, 2234)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103078 374859 457997 254417 974961 173218 489086 682944 299795 842862 773497 538337 880197 282605 580782 511424 263743 563651 939729 455607 877969 > 9¹³¹ [i]