MinT - Best Known (129−66, 129, s)-Nets in Base 9

Best Known (129−66, 129, s)-Nets in Base 9

(129−66, 129, 138)-Net over F₉ — Constructive and digital

Digital (63, 129, 138)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 46, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 83, 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]

(129−66, 129, 221)-Net over F₉ — Digital

Digital (63, 129, 221)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−66, 129, 8820)-Net in Base 9 — Upper bound on s

There is no (63, 129, 8821)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1253 171463 103993 985650 842111 716528 050691 301619 861852 308136 733889 522653 193644 695289 225966 432555 706437 592639 614505 373350 020265 > 9¹²⁹ [i]