MinT - Best Known (28, 28+69, s)-Nets in Base 27

Best Known (28, 28+69, s)-Nets in Base 27

(28, 28+69, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 97, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 97, 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+69, 116)-Net in Base 27 — Constructive

(28, 97, 116)-net in base 27, using

7 times m-reduction [i] based on (28, 104, 116)-net in base 27, using
- base change [i] based on digital (2, 78, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(28, 28+69, 208)-Net over F₂₇ — Digital

Digital (28, 97, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 97, 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+69, 5710)-Net in Base 27 — Upper bound on s

There is no (28, 97, 5711)-net in base 27, because

1 times m-reduction [i] would yield (28, 96, 5711)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 258870 048340 974444 288106 695081 134826 055263 910988 763977 795245 177104 571291 737757 177430 880129 301992 807075 656400 453673 029737 046537 699424 999725 > 27⁹⁶ [i]