MinT - Best Known (40, 110, s)-Nets in Base 27

Best Known (40, 110, s)-Nets in Base 27

(40, 110, 114)-Net over F₂₇ — Constructive and digital

Digital (40, 110, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 110, 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]

(40, 110, 172)-Net in Base 27 — Constructive

(40, 110, 172)-net in base 27, using

27² times duplication [i] based on (38, 108, 172)-net in base 27, using
- t-expansion [i] based on (34, 108, 172)-net in base 27, using
  - base change [i] based on digital (7, 81, 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]

(40, 110, 273)-Net over F₂₇ — Digital

Digital (40, 110, 273)-net over F₂₇, using

net from sequence [i] based on digital (40, 272)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 40 and N(F) ≥ 273, using
  - a curve from the manYPoints database [i]

(40, 110, 16841)-Net in Base 27 — Upper bound on s

There is no (40, 110, 16842)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 194056 727995 207656 452235 634786 447948 696018 556202 293980 988789 524583 896430 364070 157992 029517 698167 895591 664336 134201 904378 269647 284381 632332 858797 089043 451105 > 27¹¹⁰ [i]