MinT - Best Known (52, 52+88, s)-Nets in Base 9

Best Known (52, 52+88, s)-Nets in Base 9

(52, 52+88, 81)-Net over F₉ — Constructive and digital

Digital (52, 140, 81)-net over F₉, using

t-expansion [i] based on digital (32, 140, 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+88, 182)-Net over F₉ — Digital

Digital (52, 140, 182)-net over F₉, using

t-expansion [i] based on digital (50, 140, 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+88, 2317)-Net in Base 9 — Upper bound on s

There is no (52, 140, 2318)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 528130 375747 868103 865348 358022 827641 460965 612872 318608 136309 070780 767629 169239 706683 909143 208195 478790 293679 303684 368434 893671 134145 > 9¹⁴⁰ [i]