MinT - Best Known (82−62, 82, s)-Nets in Base 9

Best Known (82−62, 82, s)-Nets in Base 9

(82−62, 82, 74)-Net over F₉ — Constructive and digital

Digital (20, 82, 74)-net over F₉, using

t-expansion [i] based on digital (17, 82, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(82−62, 82, 84)-Net over F₉ — Digital

Digital (20, 82, 84)-net over F₉, using

t-expansion [i] based on digital (19, 82, 84)-net over F₉, using
- net from sequence [i] based on digital (19, 83)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
    - Drinfeld modules of rank 1 [i]

(82−62, 82, 500)-Net in Base 9 — Upper bound on s

There is no (20, 82, 501)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 855475 789326 688131 856989 263172 045457 080653 836565 999905 417681 570487 663837 964569 > 9⁸² [i]