MinT - Best Known (97−25, 97, s)-Nets in Base 9

Best Known (97−25, 97, s)-Nets in Base 9

(97−25, 97, 768)-Net over F₉ — Constructive and digital

Digital (72, 97, 768)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 15, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (57, 82, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 41, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(97−25, 97, 8822)-Net over F₉ — Digital

Digital (72, 97, 8822)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−25, 97, large)-Net in Base 9 — Upper bound on s

There is no (72, 97, large)-net in base 9, because

23 times m-reduction [i] would yield (72, 74, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]