MinT - Best Known (160−119, 160, s)-Nets in Base 8

Best Known (160−119, 160, s)-Nets in Base 8

(160−119, 160, 98)-Net over F₈ — Constructive and digital

Digital (41, 160, 98)-net over F₈, using

t-expansion [i] based on digital (37, 160, 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]

(160−119, 160, 129)-Net over F₈ — Digital

Digital (41, 160, 129)-net over F₈, using

t-expansion [i] based on digital (38, 160, 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]

(160−119, 160, 848)-Net in Base 8 — Upper bound on s

There is no (41, 160, 849)-net in base 8, because

1 times m-reduction [i] would yield (41, 159, 849)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 413175 953397 844706 737471 498992 919876 309758 453231 287384 568387 044823 256848 443432 022462 904460 896239 737772 558097 726831 452640 738386 297609 487521 194176 > 8¹⁵⁹ [i]