MinT - Best Known (60, 110, s)-Nets in Base 27

Best Known (60, 110, s)-Nets in Base 27

(60, 110, 234)-Net over F₂₇ — Constructive and digital

Digital (60, 110, 234)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (6, 22, 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. digital (6, 31, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)
3. digital (7, 57, 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]

(60, 110, 370)-Net in Base 27 — Constructive

(60, 110, 370)-net in base 27, using

27² times duplication [i] based on (58, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
  - base change [i] based on digital (16, 81, 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]

(60, 110, 1226)-Net over F₂₇ — Digital

Digital (60, 110, 1226)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 110, 777402)-Net in Base 27 — Upper bound on s

There is no (60, 110, 777403)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 185409 415039 022174 651700 676723 996524 664395 874675 076147 376806 500260 716422 623791 620395 073975 729573 804347 397800 763825 779808 576392 558417 497609 122179 339639 409103 > 27¹¹⁰ [i]