MinT - Best Known (52, 52+93, s)-Nets in Base 9

Best Known (52, 52+93, s)-Nets in Base 9

(52, 52+93, 81)-Net over F₉ — Constructive and digital

Digital (52, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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+93, 182)-Net over F₉ — Digital

Digital (52, 145, 182)-net over F₉, using

t-expansion [i] based on digital (50, 145, 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+93, 2156)-Net in Base 9 — Upper bound on s

There is no (52, 145, 2157)-net in base 9, because

1 times m-reduction [i] would yield (52, 144, 2157)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261606 813957 795090 970358 928731 298560 286627 218284 989589 365651 993725 773185 821932 700168 699367 668056 674174 915174 943677 987023 817484 261526 694641 > 9¹⁴⁴ [i]