MinT - Best Known (162−119, 162, s)-Nets in Base 8

Best Known (162−119, 162, s)-Nets in Base 8

(162−119, 162, 98)-Net over F₈ — Constructive and digital

Digital (43, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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]

(162−119, 162, 129)-Net over F₈ — Digital

Digital (43, 162, 129)-net over F₈, using

t-expansion [i] based on digital (38, 162, 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]

(162−119, 162, 912)-Net in Base 8 — Upper bound on s

There is no (43, 162, 913)-net in base 8, because

1 times m-reduction [i] would yield (43, 161, 913)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 360736 556210 397372 779031 044450 023069 123106 972170 860093 457493 254543 264717 515609 429365 301747 063486 177360 241319 119324 645213 356333 388684 845945 058688 > 8¹⁶¹ [i]