MinT - Best Known (81−65, 81, s)-Nets in Base 27

Best Known (81−65, 81, s)-Nets in Base 27

(81−65, 81, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 81, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 81, 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]

(81−65, 81, 144)-Net over F₂₇ — Digital

Digital (16, 81, 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]

(81−65, 81, 1846)-Net in Base 27 — Upper bound on s

There is no (16, 81, 1847)-net in base 27, because

1 times m-reduction [i] would yield (16, 80, 1847)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 243303 858766 335448 874749 923314 707300 663677 590406 069936 545104 343893 378908 657023 533411 597466 266988 310797 894050 007745 > 27⁸⁰ [i]