MinT - Best Known (138−106, 138, s)-Nets in Base 8

Best Known (138−106, 138, s)-Nets in Base 8

(138−106, 138, 65)-Net over F₈ — Constructive and digital

Digital (32, 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]

(138−106, 138, 97)-Net over F₈ — Digital

Digital (32, 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]

(138−106, 138, 627)-Net in Base 8 — Upper bound on s

There is no (32, 138, 628)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42875 404214 353455 334295 815216 680589 460880 178317 488944 123760 062943 109915 045331 287515 481347 877804 381146 916633 175342 986890 363824 > 8¹³⁸ [i]