MinT - Best Known (40, 40+127, s)-Nets in Base 8

Best Known (40, 40+127, s)-Nets in Base 8

(40, 40+127, 98)-Net over F₈ — Constructive and digital

Digital (40, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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+127, 129)-Net over F₈ — Digital

Digital (40, 167, 129)-net over F₈, using

t-expansion [i] based on digital (38, 167, 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+127, 792)-Net in Base 8 — Upper bound on s

There is no (40, 167, 793)-net in base 8, because

1 times m-reduction [i] would yield (40, 166, 793)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 843027 967201 669132 646803 989762 924871 722131 268793 210471 456279 412653 843409 791016 292596 585472 491557 711956 089556 316308 581369 075500 666557 860476 361712 667392 > 8¹⁶⁶ [i]