MinT - Best Known (81−67, 81, s)-Nets in Base 27

Best Known (81−67, 81, s)-Nets in Base 27

(81−67, 81, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 81, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 81, 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]

(81−67, 81, 136)-Net over F₂₇ — Digital

Digital (14, 81, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 81, 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]

(81−67, 81, 1476)-Net in Base 27 — Upper bound on s

There is no (14, 81, 1477)-net in base 27, because

1 times m-reduction [i] would yield (14, 80, 1477)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 244603 348291 433669 286151 213658 880959 061692 023337 494051 226325 296069 699635 445542 423252 516662 047947 710914 400246 068355 > 27⁸⁰ [i]