MinT - Best Known (105−53, 105, s)-Nets in Base 9

Best Known (105−53, 105, s)-Nets in Base 9

(105−53, 105, 128)-Net over F₉ — Constructive and digital

Digital (52, 105, 128)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 39, 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, 66, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(105−53, 105, 198)-Net over F₉ — Digital

Digital (52, 105, 198)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−53, 105, 8637)-Net in Base 9 — Upper bound on s

There is no (52, 105, 8638)-net in base 9, because

1 times m-reduction [i] would yield (52, 104, 8638)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1745 912486 871169 231238 915633 109760 392783 780082 087825 673563 999974 152263 460972 966842 432859 417742 832545 > 9¹⁰⁴ [i]