MinT - Best Known (172−134, 172, s)-Nets in Base 8

Best Known (172−134, 172, s)-Nets in Base 8

(172−134, 172, 98)-Net over F₈ — Constructive and digital

Digital (38, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 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]

(172−134, 172, 129)-Net over F₈ — Digital

Digital (38, 172, 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]

(172−134, 172, 724)-Net in Base 8 — Upper bound on s

There is no (38, 172, 725)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 216818 533602 965909 550758 289715 215775 517761 307669 844645 866927 026566 751129 636259 464855 816518 678924 995516 666627 289734 679524 058478 727081 087613 624340 198195 681812 > 8¹⁷² [i]