MinT - Best Known (21, 21+56, s)-Nets in Base 27

Best Known (21, 21+56, s)-Nets in Base 27

(21, 21+56, 108)-Net over F₂₇ — Constructive and digital

Digital (21, 77, 108)-net over F₂₇, using

t-expansion [i] based on digital (18, 77, 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]

(21, 21+56, 163)-Net over F₂₇ — Digital

Digital (21, 77, 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]

(21, 21+56, 3737)-Net in Base 27 — Upper bound on s

There is no (21, 77, 3738)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 164 551043 355264 521361 177329 058746 085620 588287 566205 219349 893090 925308 850503 277760 158649 321556 457592 043644 339993 > 27⁷⁷ [i]