MinT - Best Known (75−49, 75, s)-Nets in Base 27

Best Known (75−49, 75, s)-Nets in Base 27

(75−49, 75, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 75, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 75, 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]

(75−49, 75, 172)-Net in Base 27 — Constructive

(26, 75, 172)-net in base 27, using

1 times m-reduction [i] based on (26, 76, 172)-net in base 27, using
- base change [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(75−49, 75, 208)-Net over F₂₇ — Digital

Digital (26, 75, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 75, 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]

(75−49, 75, 9754)-Net in Base 27 — Upper bound on s

There is no (26, 75, 9755)-net in base 27, because

1 times m-reduction [i] would yield (26, 74, 9755)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 8343 933832 257967 477180 958303 795984 255594 599062 484325 307912 994371 572407 669087 201102 992273 778991 680035 453201 > 27⁷⁴ [i]