MinT - Best Known (109−92, 109, s)-Nets in Base 27

Best Known (109−92, 109, s)-Nets in Base 27

(109−92, 109, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 109, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 109, 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]

(109−92, 109, 144)-Net over F₂₇ — Digital

Digital (17, 109, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 109, 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]

(109−92, 109, 1681)-Net in Base 27 — Upper bound on s

There is no (17, 109, 1682)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 050766 447861 973887 912125 700550 618539 686953 529055 277652 631960 637456 436965 885631 276602 227218 727469 985635 156790 879925 629099 520882 000609 302167 662106 450573 929581 > 27¹⁰⁹ [i]