MinT - Best Known (87−73, 87, s)-Nets in Base 27

Best Known (87−73, 87, s)-Nets in Base 27

(87−73, 87, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 87, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 87, 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]

(87−73, 87, 136)-Net over F₂₇ — Digital

Digital (14, 87, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 87, 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]

(87−73, 87, 1423)-Net in Base 27 — Upper bound on s

There is no (14, 87, 1424)-net in base 27, because

1 times m-reduction [i] would yield (14, 86, 1424)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1259 651615 586113 170784 948452 306131 641640 920597 978522 964355 598188 332269 652831 140670 131943 390442 966948 987528 453691 669825 935745 > 27⁸⁶ [i]