MinT - Best Known (76−62, 76, s)-Nets in Base 27

Best Known (76−62, 76, s)-Nets in Base 27

(76−62, 76, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 76, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 76, 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]

(76−62, 76, 136)-Net over F₂₇ — Digital

Digital (14, 76, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 76, 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]

(76−62, 76, 1526)-Net in Base 27 — Upper bound on s

There is no (14, 76, 1527)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 163723 118637 769081 754891 497100 460594 043177 201019 126872 892358 250249 346169 341318 954828 410233 321706 897096 901243 > 27⁷⁶ [i]