MinT - Best Known (116−79, 116, s)-Nets in Base 8

Best Known (116−79, 116, s)-Nets in Base 8

(116−79, 116, 98)-Net over F₈ — Constructive and digital

Digital (37, 116, 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]

(116−79, 116, 121)-Net over F₈ — Digital

Digital (37, 116, 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]

(116−79, 116, 987)-Net in Base 8 — Upper bound on s

There is no (37, 116, 988)-net in base 8, because

1 times m-reduction [i] would yield (37, 115, 988)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 72 081637 581739 806467 969081 445172 568497 484574 151330 431988 310264 187152 261125 338720 606733 551698 920236 817308 > 8¹¹⁵ [i]