MinT - Best Known (55, 148, s)-Nets in Base 9

Best Known (55, 148, s)-Nets in Base 9

(55, 148, 81)-Net over F₉ — Constructive and digital

Digital (55, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(55, 148, 182)-Net over F₉ — Digital

Digital (55, 148, 182)-net over F₉, using

t-expansion [i] based on digital (50, 148, 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]

(55, 148, 2492)-Net in Base 9 — Upper bound on s

There is no (55, 148, 2493)-net in base 9, because

1 times m-reduction [i] would yield (55, 147, 2493)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 438876 053538 466067 630136 525419 046078 616173 920369 839758 364560 472212 950163 807746 006502 803275 312478 181356 082915 956791 882829 378017 017806 940145 > 9¹⁴⁷ [i]