MinT - Best Known (111−67, 111, s)-Nets in Base 8

Best Known (111−67, 111, s)-Nets in Base 8

(111−67, 111, 98)-Net over F₈ — Constructive and digital

Digital (44, 111, 98)-net over F₈, using

t-expansion [i] based on digital (37, 111, 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]

(111−67, 111, 130)-Net over F₈ — Digital

Digital (44, 111, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(111−67, 111, 1904)-Net in Base 8 — Upper bound on s

There is no (44, 111, 1905)-net in base 8, because

1 times m-reduction [i] would yield (44, 110, 1905)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2190 658366 256118 931612 709780 401499 057038 741494 686925 687351 322412 495504 533184 335471 826758 437119 893560 > 8¹¹⁰ [i]