MinT - Best Known (63−39, 63, s)-Nets in Base 27

Best Known (63−39, 63, s)-Nets in Base 27

(63−39, 63, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 63, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 63, 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]

(63−39, 63, 172)-Net in Base 27 — Constructive

(24, 63, 172)-net in base 27, using

5 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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]

(63−39, 63, 208)-Net over F₂₇ — Digital

Digital (24, 63, 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]

(63−39, 63, 226)-Net in Base 27

(24, 63, 226)-net in base 27, using

1 times m-reduction [i] based on (24, 64, 226)-net in base 27, using
- base change [i] based on digital (8, 48, 226)-net over F₈₁, using
  - net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
      - a curve from the manYPoints database [i]

(63−39, 63, 14279)-Net in Base 27 — Upper bound on s

There is no (24, 63, 14280)-net in base 27, because

1 times m-reduction [i] would yield (24, 62, 14280)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 55571 867246 500352 884086 857683 807425 990177 465770 616094 866282 817992 344402 003986 895350 338913 > 27⁶² [i]