MinT - Best Known (53, 53+93, s)-Nets in Base 9

Best Known (53, 53+93, s)-Nets in Base 9

(53, 53+93, 81)-Net over F₉ — Constructive and digital

Digital (53, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(53, 53+93, 182)-Net over F₉ — Digital

Digital (53, 146, 182)-net over F₉, using

t-expansion [i] based on digital (50, 146, 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]

(53, 53+93, 2263)-Net in Base 9 — Upper bound on s

There is no (53, 146, 2264)-net in base 9, because

1 times m-reduction [i] would yield (53, 145, 2264)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 359047 794933 982434 138915 465736 904660 527237 171590 559499 595277 297475 266316 575664 518335 251703 336243 040161 752107 700191 796196 542515 415025 915777 > 9¹⁴⁵ [i]