MinT - Best Known (120−63, 120, s)-Nets in Base 9

Best Known (120−63, 120, s)-Nets in Base 9

(120−63, 120, 128)-Net over F₉ — Constructive and digital

Digital (57, 120, 128)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 44, 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 (13, 76, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(120−63, 120, 186)-Net over F₉ — Digital

Digital (57, 120, 186)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−63, 120, 7126)-Net in Base 9 — Upper bound on s

There is no (57, 120, 7127)-net in base 9, because

1 times m-reduction [i] would yield (57, 119, 7127)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 360128 867208 124519 306986 718564 862689 459215 534929 317358 615299 663826 540393 866618 733688 432145 186637 565227 144539 143497 > 9¹¹⁹ [i]