MinT - Best Known (95−81, 95, s)-Nets in Base 27

Best Known (95−81, 95, s)-Nets in Base 27

(95−81, 95, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 95, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 95, 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]

(95−81, 95, 136)-Net over F₂₇ — Digital

Digital (14, 95, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 95, 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]

(95−81, 95, 1380)-Net in Base 27 — Upper bound on s

There is no (14, 95, 1381)-net in base 27, because

1 times m-reduction [i] would yield (14, 94, 1381)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 360 432896 968002 948188 151345 982474 845386 066865 992550 732975 076718 906416 549920 192738 654439 586035 832615 158016 147664 921588 939567 739781 882145 > 27⁹⁴ [i]