MinT - Best Known (90−73, 90, s)-Nets in Base 27

Best Known (90−73, 90, s)-Nets in Base 27

(90−73, 90, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 90, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 90, 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]

(90−73, 90, 144)-Net over F₂₇ — Digital

Digital (17, 90, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 90, 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]

(90−73, 90, 1879)-Net in Base 27 — Upper bound on s

There is no (17, 90, 1880)-net in base 27, because

1 times m-reduction [i] would yield (17, 89, 1880)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 24 780594 677717 243160 057080 119231 150866 912132 967524 443015 353068 691356 947783 619455 319563 009190 596404 663458 568330 697304 508082 171073 > 27⁸⁹ [i]