MinT - Best Known (40, 40+89, s)-Nets in Base 8

Best Known (40, 40+89, s)-Nets in Base 8

(40, 40+89, 98)-Net over F₈ — Constructive and digital

Digital (40, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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+89, 129)-Net over F₈ — Digital

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

t-expansion [i] based on digital (38, 129, 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+89, 1017)-Net in Base 8 — Upper bound on s

There is no (40, 129, 1018)-net in base 8, because

1 times m-reduction [i] would yield (40, 128, 1018)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 40 844183 653488 737110 880111 835690 879041 285341 463604 346222 214979 017066 453675 914334 470480 815988 754185 587813 213289 932300 > 8¹²⁸ [i]