MinT - Best Known (28, 28+57, s)-Nets in Base 27

Best Known (28, 28+57, s)-Nets in Base 27

(28, 28+57, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 85, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 85, 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]

(28, 28+57, 160)-Net in Base 27 — Constructive

(28, 85, 160)-net in base 27, using

7 times m-reduction [i] based on (28, 92, 160)-net in base 27, using
- base change [i] based on digital (5, 69, 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]

(28, 28+57, 208)-Net over F₂₇ — Digital

Digital (28, 85, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 85, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(28, 28+57, 8538)-Net in Base 27 — Upper bound on s

There is no (28, 85, 8539)-net in base 27, because

1 times m-reduction [i] would yield (28, 84, 8539)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 718867 588800 345514 480845 379397 112546 130303 298187 904446 334003 461446 207068 177891 168992 936211 428919 053006 203976 359053 333769 > 27⁸⁴ [i]