MinT - Best Known (97, 97+48, s)-Nets in Base 9

Best Known (97, 97+48, s)-Nets in Base 9

(97, 97+48, 740)-Net over F₉ — Constructive and digital

Digital (97, 145, 740)-net over F₉, using

t-expansion [i] based on digital (91, 145, 740)-net over F₉, using
- 5 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(97, 97+48, 2042)-Net over F₉ — Digital

Digital (97, 145, 2042)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+48, 713639)-Net in Base 9 — Upper bound on s

There is no (97, 145, 713640)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 318281 785674 090843 395939 131740 452819 229955 958291 626433 047058 674125 818501 878078 452551 714831 695703 324186 334028 247300 709789 479814 412747 031041 > 9¹⁴⁵ [i]