MinT - Best Known (67−53, 67, s)-Nets in Base 27

Best Known (67−53, 67, s)-Nets in Base 27

(67−53, 67, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 67, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 67, 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]

(67−53, 67, 136)-Net over F₂₇ — Digital

Digital (14, 67, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 67, 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]

(67−53, 67, 1731)-Net in Base 27 — Upper bound on s

There is no (14, 67, 1732)-net in base 27, because

1 times m-reduction [i] would yield (14, 66, 1732)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 29747 610927 353401 126921 522237 752704 711416 989564 741313 540591 817390 552365 981423 030995 768942 821433 > 27⁶⁶ [i]