MinT - Best Known (40, 40+119, s)-Nets in Base 8

Best Known (40, 40+119, s)-Nets in Base 8

(40, 40+119, 98)-Net over F₈ — Constructive and digital

Digital (40, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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, 40+119, 129)-Net over F₈ — Digital

Digital (40, 159, 129)-net over F₈, using

t-expansion [i] based on digital (38, 159, 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, 40+119, 817)-Net in Base 8 — Upper bound on s

There is no (40, 159, 818)-net in base 8, because

1 times m-reduction [i] would yield (40, 158, 818)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 50466 077310 751641 701297 731871 514255 697554 772487 425499 276360 643532 425765 718871 965214 044447 851675 117327 665009 541273 389905 676735 810962 390219 386752 > 8¹⁵⁸ [i]