MinT - Best Known (144−84, 144, s)-Nets in Base 9

Best Known (144−84, 144, s)-Nets in Base 9

(144−84, 144, 96)-Net over F₉ — Constructive and digital

Digital (60, 144, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 47, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 97, 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]

(144−84, 144, 190)-Net over F₉ — Digital

Digital (60, 144, 190)-net over F₉, using

net from sequence [i] based on digital (60, 189)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 60 and N(F) ≥ 190, using
  - Drinfeld modules of rank 1 [i]

(144−84, 144, 3832)-Net in Base 9 — Upper bound on s

There is no (60, 144, 3833)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258596 442324 899917 402385 332233 629501 574484 367900 423098 014194 896703 868728 608556 229637 504727 538056 846178 001587 446948 774203 687894 514765 152017 > 9¹⁴⁴ [i]