MinT - Best Known (41, 41+93, s)-Nets in Base 8

Best Known (41, 41+93, s)-Nets in Base 8

(41, 41+93, 98)-Net over F₈ — Constructive and digital

Digital (41, 134, 98)-net over F₈, using

t-expansion [i] based on digital (37, 134, 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]

(41, 41+93, 129)-Net over F₈ — Digital

Digital (41, 134, 129)-net over F₈, using

t-expansion [i] based on digital (38, 134, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(41, 41+93, 1021)-Net in Base 8 — Upper bound on s

There is no (41, 134, 1022)-net in base 8, because

1 times m-reduction [i] would yield (41, 133, 1022)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 331758 229374 953102 887280 718904 379042 669057 830439 292422 413919 132261 423787 069911 260249 712921 154406 091898 533063 993683 488920 > 8¹³³ [i]