MinT - Best Known (160−120, 160, s)-Nets in Base 8

Best Known (160−120, 160, s)-Nets in Base 8

(160−120, 160, 98)-Net over F₈ — Constructive and digital

Digital (40, 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]

(160−120, 160, 129)-Net over F₈ — Digital

Digital (40, 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]

(160−120, 160, 810)-Net in Base 8 — Upper bound on s

There is no (40, 160, 811)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 212003 055552 939170 933352 873252 654043 474237 572798 965311 887954 446865 704975 972588 467395 869415 345165 328078 531372 011558 256289 387490 534722 162257 904704 > 8¹⁶⁰ [i]