MinT - Best Known (54−40, 54, s)-Nets in Base 27

Best Known (54−40, 54, s)-Nets in Base 27

(54−40, 54, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 54, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 54, 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]

(54−40, 54, 136)-Net over F₂₇ — Digital

Digital (14, 54, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 54, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(54−40, 54, 2328)-Net in Base 27 — Upper bound on s

There is no (14, 54, 2329)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 197200 544609 959974 849794 149090 381590 197479 822373 814370 642091 796672 250419 111921 > 27⁵⁴ [i]