MinT - Best Known (59, 97, s)-Nets in Base 27

Best Known (59, 97, s)-Nets in Base 27

(59, 97, 274)-Net over F₂₇ — Constructive and digital

Digital (59, 97, 274)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 13, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (4, 16, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
3. digital (4, 23, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
4. digital (7, 45, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(59, 97, 446)-Net in Base 27 — Constructive

(59, 97, 446)-net in base 27, using

(u,Â u+v)-construction [i] based on
1. digital (6, 25, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. (34, 72, 370)-net in base 27, using
  - base change [i] based on digital (16, 54, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(59, 97, 3206)-Net over F₂₇ — Digital

Digital (59, 97, 3206)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 97, 6190563)-Net in Base 27 — Upper bound on s

There is no (59, 97, 6190564)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 954823 283947 121718 108411 755395 379918 395313 776419 416573 000913 324149 830901 760688 195103 792865 117938 200596 466623 632901 779950 999718 782544 961681 > 27⁹⁷ [i]