MinT - Best Known (87−64, 87, s)-Nets in Base 27

Best Known (87−64, 87, s)-Nets in Base 27

(87−64, 87, 114)-Net over F₂₇ — Constructive and digital

Digital (23, 87, 114)-net over F₂₇, using

net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
  - an explicitly constructive algebraic function field [i]

(87−64, 87, 163)-Net over F₂₇ — Digital

Digital (23, 87, 163)-net over F₂₇, using

t-expansion [i] based on digital (21, 87, 163)-net over F₂₇, using
- net from sequence [i] based on digital (21, 162)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 21 and N(F) ≥ 163, using
    - a curve from the manYPoints database [i]

(87−64, 87, 3815)-Net in Base 27 — Upper bound on s

There is no (23, 87, 3816)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 33976 793921 765790 519663 681314 968192 931917 927902 998199 150157 163842 200913 883427 951655 209491 476194 466800 740406 177726 038247 931905 > 27⁸⁷ [i]