MinT - Best Known (13, 13+53, s)-Nets in Base 27

Best Known (13, 13+53, s)-Nets in Base 27

(13, 13+53, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 66, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 66, 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, 13+53, 136)-Net over F₂₇ — Digital

Digital (13, 66, 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, 13+53, 1523)-Net in Base 27 — Upper bound on s

There is no (13, 66, 1524)-net in base 27, because

1 times m-reduction [i] would yield (13, 65, 1524)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1098 209625 733774 548369 008432 792605 347577 564893 194811 852203 373379 933435 909188 324625 290743 662425 > 27⁶⁵ [i]