MinT - Best Known (95−65, 95, s)-Nets in Base 27

Best Known (95−65, 95, s)-Nets in Base 27

(95−65, 95, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 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]

(95−65, 95, 160)-Net in Base 27 — Constructive

(30, 95, 160)-net in base 27, using

5 times m-reduction [i] based on (30, 100, 160)-net in base 27, using
- base change [i] based on digital (5, 75, 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]

(95−65, 95, 208)-Net over F₂₇ — Digital

Digital (30, 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]

(95−65, 95, 7863)-Net in Base 27 — Upper bound on s

There is no (30, 95, 7864)-net in base 27, because

1 times m-reduction [i] would yield (30, 94, 7864)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 354 070000 031756 128051 441561 342510 178754 606501 300055 192889 935752 760831 373498 576648 940828 572347 246925 173464 161385 598847 120367 009479 690241 > 27⁹⁴ [i]