MinT - Best Known (148−87, 148, s)-Nets in Base 9

Best Known (148−87, 148, s)-Nets in Base 9

(148−87, 148, 96)-Net over F₉ — Constructive and digital

Digital (61, 148, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 48, 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, 100, 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]

(148−87, 148, 192)-Net over F₉ — Digital

Digital (61, 148, 192)-net over F₉, using

net from sequence [i] based on digital (61, 191)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
  - Drinfeld modules of rank 1 [i]

(148−87, 148, 3833)-Net in Base 9 — Upper bound on s

There is no (61, 148, 3834)-net in base 9, because

1 times m-reduction [i] would yield (61, 147, 3834)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 189 032338 970967 268203 612556 762483 401542 344944 365227 606675 317094 623727 981973 913328 652299 568876 170856 463444 417359 055938 167857 192230 025813 922353 > 9¹⁴⁷ [i]