MinT - Best Known (171−132, 171, s)-Nets in Base 8

Best Known (171−132, 171, s)-Nets in Base 8

(171−132, 171, 98)-Net over F₈ — Constructive and digital

Digital (39, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−132, 171, 129)-Net over F₈ — Digital

Digital (39, 171, 129)-net over F₈, using

t-expansion [i] based on digital (38, 171, 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]

(171−132, 171, 752)-Net in Base 8 — Upper bound on s

There is no (39, 171, 753)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27455 532443 662634 642059 488086 207661 151965 042018 585246 674484 820031 868815 303456 786371 751988 608130 069644 368961 537962 068284 748161 906182 173886 149808 733270 578056 > 8¹⁷¹ [i]