MinT - Best Known (138−109, 138, s)-Nets in Base 8

Best Known (138−109, 138, s)-Nets in Base 8

(138−109, 138, 65)-Net over F₈ — Constructive and digital

Digital (29, 138, 65)-net over F₈, using

t-expansion [i] based on digital (14, 138, 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]

(138−109, 138, 97)-Net over F₈ — Digital

Digital (29, 138, 97)-net over F₈, using

t-expansion [i] based on digital (28, 138, 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]

(138−109, 138, 551)-Net in Base 8 — Upper bound on s

There is no (29, 138, 552)-net in base 8, because

1 times m-reduction [i] would yield (29, 137, 552)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5288 463041 293238 252683 077882 783704 011880 749610 305511 045491 743786 356385 816857 787843 675537 089994 841293 846941 501384 540343 378784 > 8¹³⁷ [i]