MinT - Best Known (81−44, 81, s)-Nets in Base 8

Best Known (81−44, 81, s)-Nets in Base 8

(81−44, 81, 98)-Net over F₈ — Constructive and digital

Digital (37, 81, 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]

(81−44, 81, 121)-Net over F₈ — Digital

Digital (37, 81, 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]

(81−44, 81, 2720)-Net in Base 8 — Upper bound on s

There is no (37, 81, 2721)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 14 227548 889431 993651 262924 772224 127123 468966 823991 101089 561992 835635 410224 > 8⁸¹ [i]