MinT - Best Known (149−87, 149, s)-Nets in Base 9

Best Known (149−87, 149, s)-Nets in Base 9

(149−87, 149, 98)-Net over F₉ — Constructive and digital

Digital (62, 149, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 49, 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, 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]

(149−87, 149, 192)-Net over F₉ — Digital

Digital (62, 149, 192)-net over F₉, using

t-expansion [i] based on digital (61, 149, 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]

(149−87, 149, 4035)-Net in Base 9 — Upper bound on s

There is no (62, 149, 4036)-net in base 9, because

1 times m-reduction [i] would yield (62, 148, 4036)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1694 466570 963515 498035 751261 071533 483515 590694 501213 374742 492279 472993 046531 954433 398202 257572 568979 198576 374699 611929 201036 863955 327972 290785 > 9¹⁴⁸ [i]