MinT - Best Known (61−45, 61, s)-Nets in Base 27

Best Known (61−45, 61, s)-Nets in Base 27

(61−45, 61, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 61, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 61, 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]

(61−45, 61, 144)-Net over F₂₇ — Digital

Digital (16, 61, 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]

(61−45, 61, 2778)-Net in Base 27 — Upper bound on s

There is no (16, 61, 2779)-net in base 27, because

1 times m-reduction [i] would yield (16, 60, 2779)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 76 399214 166000 018013 394339 326167 355233 478774 310586 542163 662218 326029 986776 219930 583389 > 27⁶⁰ [i]