MinT - Best Known (66−51, 66, s)-Nets in Base 27

Best Known (66−51, 66, s)-Nets in Base 27

(66−51, 66, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 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]

(66−51, 66, 136)-Net over F₂₇ — Digital

Digital (15, 66, 136)-net over F₂₇, using

t-expansion [i] based on 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]

(66−51, 66, 2048)-Net in Base 27 — Upper bound on s

There is no (15, 66, 2049)-net in base 27, because

1 times m-reduction [i] would yield (15, 65, 2049)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1098 007108 113645 507428 556119 339703 594903 483379 970376 504279 856452 126558 456754 930877 393368 863483 > 27⁶⁵ [i]