MinT - Best Known (77−60, 77, s)-Nets in Base 27

Best Known (77−60, 77, s)-Nets in Base 27

(77−60, 77, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 77, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 77, 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]

(77−60, 77, 144)-Net over F₂₇ — Digital

Digital (17, 77, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 77, 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]

(77−60, 77, 2170)-Net in Base 27 — Upper bound on s

There is no (17, 77, 2171)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 165 497835 116191 396051 735133 347432 518787 429644 048062 529533 939621 302213 469696 100354 773733 955251 067628 890863 635853 > 27⁷⁷ [i]