MinT - Best Known (137−92, 137, s)-Nets in Base 9

Best Known (137−92, 137, s)-Nets in Base 9

(137−92, 137, 81)-Net over F₉ — Constructive and digital

Digital (45, 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]

(137−92, 137, 147)-Net over F₉ — Digital

Digital (45, 137, 147)-net over F₉, using

t-expansion [i] based on digital (43, 137, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(137−92, 137, 1535)-Net in Base 9 — Upper bound on s

There is no (45, 137, 1536)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 54671 232049 431271 589848 712086 127950 243216 036129 528994 033313 672155 454086 825797 783439 391542 617498 634273 711884 670829 839554 862231 642113 > 9¹³⁷ [i]