MinT - Best Known (82−68, 82, s)-Nets in Base 27

Best Known (82−68, 82, s)-Nets in Base 27

(82−68, 82, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 82, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 82, 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]

(82−68, 82, 136)-Net over F₂₇ — Digital

Digital (14, 82, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 82, 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]

(82−68, 82, 1456)-Net in Base 27 — Upper bound on s

There is no (14, 82, 1457)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2373 859168 662712 639026 636685 900050 931678 698114 949025 556151 373214 573220 072086 231520 739433 803877 754005 321321 548861 005625 > 27⁸² [i]