MinT - Best Known (20, 20+40, s)-Nets in Base 27

Best Known (20, 20+40, s)-Nets in Base 27

(20, 20+40, 108)-Net over F₂₇ — Constructive and digital

Digital (20, 60, 108)-net over F₂₇, using

t-expansion [i] based on digital (18, 60, 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]

(20, 20+40, 148)-Net over F₂₇ — Digital

Digital (20, 60, 148)-net over F₂₇, using

t-expansion [i] based on digital (18, 60, 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]

(20, 20+40, 160)-Net in Base 27 — Constructive

(20, 60, 160)-net in base 27, using

base change [i] based on digital (5, 45, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(20, 20+40, 167)-Net in Base 27

(20, 60, 167)-net in base 27, using

base change [i] based on digital (5, 45, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(20, 20+40, 6276)-Net in Base 27 — Upper bound on s

There is no (20, 60, 6277)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 76 309425 189065 255027 180772 126124 756468 727992 012326 219810 695658 711874 228884 319644 937521 > 27⁶⁰ [i]