MinT - Best Known (16, 16+72, s)-Nets in Base 27

Best Known (16, 16+72, s)-Nets in Base 27

(16, 16+72, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 88, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 88, 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]

(16, 16+72, 144)-Net over F₂₇ — Digital

Digital (16, 88, 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]

(16, 16+72, 1713)-Net in Base 27 — Upper bound on s

There is no (16, 88, 1714)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 920029 150292 416884 886867 484485 214067 759604 133216 037834 005683 297267 691265 743608 722981 743698 423851 349853 893488 804658 032966 616425 > 27⁸⁸ [i]