MinT - Best Known (40, 149, s)-Nets in Base 8

Best Known (40, 149, s)-Nets in Base 8

(40, 149, 98)-Net over F₈ — Constructive and digital

Digital (40, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(40, 149, 129)-Net over F₈ — Digital

Digital (40, 149, 129)-net over F₈, using

t-expansion [i] based on digital (38, 149, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(40, 149, 860)-Net in Base 8 — Upper bound on s

There is no (40, 149, 861)-net in base 8, because

1 times m-reduction [i] would yield (40, 148, 861)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 323475 819046 525429 295311 804532 128539 941641 329908 799766 009990 948476 388125 727898 262963 775950 560032 480874 885321 197766 388495 658450 761256 > 8¹⁴⁸ [i]