MinT - Best Known (96−82, 96, s)-Nets in Base 27

Best Known (96−82, 96, s)-Nets in Base 27

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

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

t-expansion [i] based on digital (11, 96, 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]

(96−82, 96, 136)-Net over F₂₇ — Digital

Digital (14, 96, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 96, 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]

(96−82, 96, 1373)-Net in Base 27 — Upper bound on s

There is no (14, 96, 1374)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 265122 624792 178510 656927 010568 216725 834129 578689 626638 494607 914953 029512 432272 484288 546463 248712 156996 622585 866949 295915 248686 683830 071485 > 27⁹⁶ [i]