MinT - Best Known (83−68, 83, s)-Nets in Base 27

Best Known (83−68, 83, s)-Nets in Base 27

(83−68, 83, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 83, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 83, 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]

(83−68, 83, 136)-Net over F₂₇ — Digital

Digital (15, 83, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 83, 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]

(83−68, 83, 1606)-Net in Base 27 — Upper bound on s

There is no (15, 83, 1607)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 63944 390345 012012 957355 025668 796066 128213 262524 288031 331951 783632 442235 157566 290594 490686 745467 570249 149666 653116 552349 > 27⁸³ [i]