MinT - Best Known (48, 107, s)-Nets in Base 9

Best Known (48, 107, s)-Nets in Base 9

(48, 107, 98)-Net over F₉ — Constructive and digital

Digital (48, 107, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 35, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (13, 72, 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]

(48, 107, 163)-Net over F₉ — Digital

Digital (48, 107, 163)-net over F₉, using

net from sequence [i] based on digital (48, 162)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 48 and N(F) ≥ 163, using
  - Drinfeld modules of rank 1 [i]

(48, 107, 4469)-Net in Base 9 — Upper bound on s

There is no (48, 107, 4470)-net in base 9, because

1 times m-reduction [i] would yield (48, 106, 4470)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141740 350071 589946 596874 476305 540380 948618 612866 560667 361286 935525 071522 893090 018373 927000 149075 397233 > 9¹⁰⁶ [i]