MinT - Best Known (109−60, 109, s)-Nets in Base 9

Best Known (109−60, 109, s)-Nets in Base 9

(109−60, 109, 98)-Net over F₉ — Constructive and digital

Digital (49, 109, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 36, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (13, 73, 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]

(109−60, 109, 168)-Net over F₉ — Digital

Digital (49, 109, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(109−60, 109, 4395)-Net in Base 9 — Upper bound on s

There is no (49, 109, 4396)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103 438321 510365 666981 832310 186409 764423 052945 519018 844762 308680 815250 269666 318408 694325 655957 122765 699009 > 9¹⁰⁹ [i]