MinT - Best Known (132−95, 132, s)-Nets in Base 9

Best Known (132−95, 132, s)-Nets in Base 9

(132−95, 132, 81)-Net over F₉ — Constructive and digital

Digital (37, 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]

(132−95, 132, 128)-Net over F₉ — Digital

Digital (37, 132, 128)-net over F₉, using

t-expansion [i] based on digital (33, 132, 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]

(132−95, 132, 1020)-Net in Base 9 — Upper bound on s

There is no (37, 132, 1021)-net in base 9, because

1 times m-reduction [i] would yield (37, 131, 1021)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 105089 075597 588318 780903 654410 205762 966541 705419 416865 868873 946156 252691 156281 576170 842161 350756 175819 854246 120062 913633 310809 > 9¹³¹ [i]