MinT - Best Known (103, 103+43, s)-Nets in Base 9

Best Known (103, 103+43, s)-Nets in Base 9

(103, 103+43, 776)-Net over F₉ — Constructive and digital

Digital (103, 146, 776)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (7, 28, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]
2. digital (75, 118, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 59, 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]

(103, 103+43, 4305)-Net over F₉ — Digital

Digital (103, 146, 4305)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+43, 4209384)-Net in Base 9 — Upper bound on s

There is no (103, 146, 4209385)-net in base 9, because

1 times m-reduction [i] would yield (103, 145, 4209385)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 318274 192948 527950 954296 658586 436314 462884 652383 260738 075229 207657 227806 418652 900288 625634 032271 948978 353046 146788 466408 714385 067547 422569 > 9¹⁴⁵ [i]