MinT - Best Known (132−91, 132, s)-Nets in Base 9

Best Known (132−91, 132, s)-Nets in Base 9

(132−91, 132, 81)-Net over F₉ — Constructive and digital

Digital (41, 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]

(132−91, 132, 140)-Net over F₉ — Digital

Digital (41, 132, 140)-net over F₉, using

t-expansion [i] based on digital (39, 132, 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]

(132−91, 132, 1293)-Net in Base 9 — Upper bound on s

There is no (41, 132, 1294)-net in base 9, because

1 times m-reduction [i] would yield (41, 131, 1294)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 102006 439613 676730 625958 573025 800243 569586 719614 302566 852540 346039 430319 294946 405595 826104 047616 025262 550550 981626 288052 100913 > 9¹³¹ [i]