MinT - Best Known (162−131, 162, s)-Nets in Base 8

Best Known (162−131, 162, s)-Nets in Base 8

(162−131, 162, 65)-Net over F₈ — Constructive and digital

Digital (31, 162, 65)-net over F₈, using

t-expansion [i] based on digital (14, 162, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(162−131, 162, 97)-Net over F₈ — Digital

Digital (31, 162, 97)-net over F₈, using

t-expansion [i] based on digital (28, 162, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(162−131, 162, 576)-Net in Base 8 — Upper bound on s

There is no (31, 162, 577)-net in base 8, because

1 times m-reduction [i] would yield (31, 161, 577)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 423113 643907 575311 443562 375650 551001 663300 816717 778372 022092 633914 683436 487063 202321 284285 637043 827878 710686 083897 304532 029152 911607 723356 115144 > 8¹⁶¹ [i]