MinT - Best Known (16, 16+66, s)-Nets in Base 27

Best Known (16, 16+66, s)-Nets in Base 27

(16, 16+66, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 82, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 82, 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+66, 144)-Net over F₂₇ — Digital

Digital (16, 82, 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+66, 1807)-Net in Base 27 — Upper bound on s

There is no (16, 82, 1808)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2392 976245 770566 616724 815563 105868 335067 657032 859182 359628 032228 044659 622195 951193 195732 136898 670993 273427 078976 644001 > 27⁸² [i]