MinT - Best Known (86−69, 86, s)-Nets in Base 27

Best Known (86−69, 86, s)-Nets in Base 27

(86−69, 86, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 86, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 86, 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]

(86−69, 86, 144)-Net over F₂₇ — Digital

Digital (17, 86, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 86, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(86−69, 86, 1954)-Net in Base 27 — Upper bound on s

There is no (17, 86, 1955)-net in base 27, because

1 times m-reduction [i] would yield (17, 85, 1955)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 940066 987633 930511 409577 508876 294735 011161 461751 227931 877065 177001 568083 774730 986289 686171 994720 433697 133646 101203 674485 > 27⁸⁵ [i]