MinT - Best Known (149−59, 149, s)-Nets in Base 9

Best Known (149−59, 149, s)-Nets in Base 9

(149−59, 149, 448)-Net over F₉ — Constructive and digital

Digital (90, 149, 448)-net over F₉, using

t-expansion [i] based on digital (88, 149, 448)-net over F₉, using
- 1 times m-reduction [i] based on digital (88, 150, 448)-net over F₉, using
  - trace code for nets [i] based on digital (13, 75, 224)-net over F₈₁, using
    - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
        a function field by SÃ©mirat [i]

(149−59, 149, 799)-Net over F₉ — Digital

Digital (90, 149, 799)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−59, 149, 108115)-Net in Base 9 — Upper bound on s

There is no (90, 149, 108116)-net in base 9, because

1 times m-reduction [i] would yield (90, 148, 108116)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1690 179415 512860 049753 553034 404605 994265 831434 633220 940895 459761 441840 102671 315143 348868 693974 433860 593562 140612 218367 738551 258708 867865 308961 > 9¹⁴⁸ [i]