MinT - Best Known (52, 52+95, s)-Nets in Base 9

Best Known (52, 52+95, s)-Nets in Base 9

(52, 52+95, 81)-Net over F₉ — Constructive and digital

Digital (52, 147, 81)-net over F₉, using

t-expansion [i] based on digital (32, 147, 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]

(52, 52+95, 182)-Net over F₉ — Digital

Digital (52, 147, 182)-net over F₉, using

t-expansion [i] based on digital (50, 147, 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]

(52, 52+95, 2085)-Net in Base 9 — Upper bound on s

There is no (52, 147, 2086)-net in base 9, because

1 times m-reduction [i] would yield (52, 146, 2086)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 885038 641097 668363 865535 058851 055865 818549 412436 547637 470597 335214 611980 472611 279096 806260 585471 068991 562942 132346 150248 732343 267872 499473 > 9¹⁴⁶ [i]