MinT - Best Known (69−50, 69, s)-Nets in Base 27

Best Known (69−50, 69, s)-Nets in Base 27

(69−50, 69, 108)-Net over F₂₇ — Constructive and digital

Digital (19, 69, 108)-net over F₂₇, using

t-expansion [i] based on digital (18, 69, 108)-net over F₂₇, using
- net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
    - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(69−50, 69, 148)-Net over F₂₇ — Digital

Digital (19, 69, 148)-net over F₂₇, using

t-expansion [i] based on digital (18, 69, 148)-net over F₂₇, using
- net from sequence [i] based on digital (18, 147)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 148, using
    - a curve from the manYPoints database [i]

(69−50, 69, 3480)-Net in Base 27 — Upper bound on s

There is no (19, 69, 3481)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 584 261492 295151 385050 307425 405736 678773 796109 816947 758187 647667 953649 323737 605320 642311 103865 160171 > 27⁶⁹ [i]