MinT - Best Known (37, 37+86, s)-Nets in Base 8

Best Known (37, 37+86, s)-Nets in Base 8

(37, 37+86, 98)-Net over F₈ — Constructive and digital

Digital (37, 123, 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+86, 121)-Net over F₈ — Digital

Digital (37, 123, 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+86, 897)-Net in Base 8 — Upper bound on s

There is no (37, 123, 898)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1259 529419 727781 253313 241603 962126 762171 687150 454742 527495 797157 057423 635505 298257 014948 786609 915963 371535 933248 > 8¹²³ [i]