MinT - Best Known (55, 55+91, s)-Nets in Base 9

Best Known (55, 55+91, s)-Nets in Base 9

(55, 55+91, 81)-Net over F₉ — Constructive and digital

Digital (55, 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]

(55, 55+91, 182)-Net over F₉ — Digital

Digital (55, 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]

(55, 55+91, 2589)-Net in Base 9 — Upper bound on s

There is no (55, 146, 2590)-net in base 9, because

1 times m-reduction [i] would yield (55, 145, 2590)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 325074 848722 595437 004327 290422 711765 180505 915813 848451 931020 649511 965139 034093 513823 861310 929255 249798 915010 378222 303542 395502 234574 408113 > 9¹⁴⁵ [i]