MinT - Best Known (159−120, 159, s)-Nets in Base 8

Best Known (159−120, 159, s)-Nets in Base 8

(159−120, 159, 98)-Net over F₈ — Constructive and digital

Digital (39, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(159−120, 159, 129)-Net over F₈ — Digital

Digital (39, 159, 129)-net over F₈, using

t-expansion [i] based on digital (38, 159, 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]

(159−120, 159, 781)-Net in Base 8 — Upper bound on s

There is no (39, 159, 782)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 398209 026122 756042 181298 077569 132722 717534 477882 353526 923242 262146 944251 199161 951593 500415 077941 169069 540856 348223 933195 251004 821576 611632 738896 > 8¹⁵⁹ [i]