MinT - Best Known (74−61, 74, s)-Nets in Base 27

Best Known (74−61, 74, s)-Nets in Base 27

(74−61, 74, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 74, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 74, 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]

(74−61, 74, 136)-Net over F₂₇ — Digital

Digital (13, 74, 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]

(74−61, 74, 1393)-Net in Base 27 — Upper bound on s

There is no (13, 74, 1394)-net in base 27, because

1 times m-reduction [i] would yield (13, 73, 1394)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 315 178116 036990 866387 607624 022256 856721 934782 586050 279895 778034 510348 738974 611262 793186 173126 732248 275725 > 27⁷³ [i]