MinT - Best Known (95−67, 95, s)-Nets in Base 27

Best Known (95−67, 95, s)-Nets in Base 27

(95−67, 95, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 95, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 95, 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]

(95−67, 95, 150)-Net in Base 27 — Constructive

(28, 95, 150)-net in base 27, using

1 times m-reduction [i] based on (28, 96, 150)-net in base 27, using
- base change [i] based on digital (4, 72, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(95−67, 95, 208)-Net over F₂₇ — Digital

Digital (28, 95, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 95, 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]

(95−67, 95, 6030)-Net in Base 27 — Upper bound on s

There is no (28, 95, 6031)-net in base 27, because

1 times m-reduction [i] would yield (28, 94, 6031)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 354 189418 826572 945354 643202 170442 009566 686871 667137 269257 138569 775554 206740 043588 976698 574105 478924 689399 497459 970619 238343 658005 975367 > 27⁹⁴ [i]