MinT - Best Known (93−67, 93, s)-Nets in Base 27

Best Known (93−67, 93, s)-Nets in Base 27

(93−67, 93, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 93, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 93, 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]

(93−67, 93, 116)-Net in Base 27 — Constructive

(26, 93, 116)-net in base 27, using

3 times m-reduction [i] based on (26, 96, 116)-net in base 27, using
- base change [i] based on digital (2, 72, 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]

(93−67, 93, 208)-Net over F₂₇ — Digital

Digital (26, 93, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 93, 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]

(93−67, 93, 4935)-Net in Base 27 — Upper bound on s

There is no (26, 93, 4936)-net in base 27, because

1 times m-reduction [i] would yield (26, 92, 4936)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 486216 683836 783772 461254 504858 801373 145565 372888 496668 114842 962359 599912 932601 373895 024746 447375 478354 301017 056718 916242 787323 260753 > 27⁹² [i]