MinT - Best Known (110−73, 110, s)-Nets in Base 9

Best Known (110−73, 110, s)-Nets in Base 9

(110−73, 110, 81)-Net over F₉ — Constructive and digital

Digital (37, 110, 81)-net over F₉, using

t-expansion [i] based on digital (32, 110, 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]

(110−73, 110, 128)-Net over F₉ — Digital

Digital (37, 110, 128)-net over F₉, using

t-expansion [i] based on digital (33, 110, 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]

(110−73, 110, 1361)-Net in Base 9 — Upper bound on s

There is no (37, 110, 1362)-net in base 9, because

1 times m-reduction [i] would yield (37, 109, 1362)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104 820744 626249 820816 927988 635316 359031 449415 864247 364309 925079 037649 648639 471782 715193 476276 765868 658881 > 9¹⁰⁹ [i]