MinT - Best Known (39, 39+52, s)-Nets in Base 27

Best Known (39, 39+52, s)-Nets in Base 27

(39, 39+52, 158)-Net over F₂₇ — Constructive and digital

Digital (39, 91, 158)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 32, 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 (7, 59, 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]

(39, 39+52, 271)-Net over F₂₇ — Digital

Digital (39, 91, 271)-net over F₂₇, using

net from sequence [i] based on digital (39, 270)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 39 and N(F) ≥ 271, using
  - a curve from the manYPoints database [i]

(39, 39+52, 370)-Net in Base 27 — Constructive

(39, 91, 370)-net in base 27, using

1 times m-reduction [i] based on (39, 92, 370)-net in base 27, using
- base change [i] based on digital (16, 69, 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]

(39, 39+52, 41490)-Net in Base 27 — Upper bound on s

There is no (39, 91, 41491)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 17954 056834 670273 348674 330124 157753 619951 491247 780669 004000 231234 605234 719527 921611 211392 271363 301955 042458 593320 806484 235101 922277 > 27⁹¹ [i]