MinT - Best Known (85−71, 85, s)-Nets in Base 27

Best Known (85−71, 85, s)-Nets in Base 27

(85−71, 85, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 85, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 85, 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]

(85−71, 85, 136)-Net over F₂₇ — Digital

Digital (14, 85, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 85, 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]

(85−71, 85, 1439)-Net in Base 27 — Upper bound on s

There is no (14, 85, 1440)-net in base 27, because

1 times m-reduction [i] would yield (14, 84, 1440)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 755590 549214 715650 560184 308417 168185 580890 366650 517717 515478 988938 490485 295422 717932 880563 207441 879222 617386 696752 341377 > 27⁸⁴ [i]