MinT - Best Known (37, 37+114, s)-Nets in Base 8

Best Known (37, 37+114, s)-Nets in Base 8

(37, 37+114, 98)-Net over F₈ — Constructive and digital

Digital (37, 151, 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]

(37, 37+114, 121)-Net over F₈ — Digital

Digital (37, 151, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 37+114, 742)-Net in Base 8 — Upper bound on s

There is no (37, 151, 743)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23397 445436 158974 828606 943920 759848 738828 931629 182355 287566 092906 709724 819316 385620 394449 052582 794072 945336 818792 737523 263506 353775 271888 > 8¹⁵¹ [i]