MinT - Best Known (19, 19+64, s)-Nets in Base 27

Best Known (19, 19+64, s)-Nets in Base 27

(19, 19+64, 108)-Net over F₂₇ — Constructive and digital

Digital (19, 83, 108)-net over F₂₇, using

t-expansion [i] based on digital (18, 83, 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]

(19, 19+64, 148)-Net over F₂₇ — Digital

Digital (19, 83, 148)-net over F₂₇, using

t-expansion [i] based on digital (18, 83, 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]

(19, 19+64, 2521)-Net in Base 27 — Upper bound on s

There is no (19, 83, 2522)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 64058 037881 730655 812903 952844 666159 666031 109990 465376 839262 043877 764736 506109 099751 778205 842457 682552 821571 287966 395201 > 27⁸³ [i]