MinT - Best Known (13, 56, s)-Nets in Base 27

Best Known (13, 56, s)-Nets in Base 27

(13, 56, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 56, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 56, 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]

(13, 56, 136)-Net over F₂₇ — Digital

Digital (13, 56, 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]

(13, 56, 1861)-Net in Base 27 — Upper bound on s

There is no (13, 56, 1862)-net in base 27, because

1 times m-reduction [i] would yield (13, 55, 1862)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5 350370 625702 906892 337199 440224 245978 392857 547380 851060 195652 809567 197307 032917 > 27⁵⁵ [i]