MinT - Best Known (55−43, 55, s)-Nets in Base 27

Best Known (55−43, 55, s)-Nets in Base 27

(55−43, 55, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 55, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 55, 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]

(55−43, 55, 109)-Net over F₂₇ — Digital

Digital (12, 55, 109)-net over F₂₇, using

net from sequence [i] based on digital (12, 108)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 12 and N(F) ≥ 109, using
  - a curve from the manYPoints database [i]

(55−43, 55, 1589)-Net in Base 27 — Upper bound on s

There is no (12, 55, 1590)-net in base 27, because

1 times m-reduction [i] would yield (12, 54, 1590)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 198209 211927 978420 881415 028956 706270 375419 993763 479138 627952 598016 703971 753269 > 27⁵⁴ [i]