MinT - Best Known (137−90, 137, s)-Nets in Base 9

Best Known (137−90, 137, s)-Nets in Base 9

(137−90, 137, 81)-Net over F₉ — Constructive and digital

Digital (47, 137, 81)-net over F₉, using

t-expansion [i] based on digital (32, 137, 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]

(137−90, 137, 162)-Net over F₉ — Digital

Digital (47, 137, 162)-net over F₉, using

t-expansion [i] based on digital (46, 137, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(137−90, 137, 1743)-Net in Base 9 — Upper bound on s

There is no (47, 137, 1744)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 54523 670375 514171 950499 673769 336662 321927 127700 910951 527191 339730 547257 867647 360523 396093 651673 149695 536787 560548 393542 450069 790849 > 9¹³⁷ [i]