MinT - Best Known (96−81, 96, s)-Nets in Base 27

Best Known (96−81, 96, s)-Nets in Base 27

(96−81, 96, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 96, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 96, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(96−81, 96, 136)-Net over F₂₇ — Digital

Digital (15, 96, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 96, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(96−81, 96, 1500)-Net in Base 27 — Upper bound on s

There is no (15, 96, 1501)-net in base 27, because

1 times m-reduction [i] would yield (15, 95, 1501)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9629 034198 772626 750059 955939 679038 132218 456372 460503 704468 322105 834083 114943 204992 753194 768064 132527 857070 814745 602883 502826 410777 339681 > 27⁹⁵ [i]