MinT - Best Known (80−60, 80, s)-Nets in Base 9

Best Known (80−60, 80, s)-Nets in Base 9

(80−60, 80, 74)-Net over F₉ — Constructive and digital

Digital (20, 80, 74)-net over F₉, using

t-expansion [i] based on digital (17, 80, 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]

(80−60, 80, 84)-Net over F₉ — Digital

Digital (20, 80, 84)-net over F₉, using

t-expansion [i] based on digital (19, 80, 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]

(80−60, 80, 509)-Net in Base 9 — Upper bound on s

There is no (20, 80, 510)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22370 645032 373040 949647 812893 916759 868186 942800 721182 518416 925688 882438 343393 > 9⁸⁰ [i]