MinT - Best Known (40, 96, s)-Nets in Base 27

Best Known (40, 96, s)-Nets in Base 27

(40, 96, 152)-Net over F₂₇ — Constructive and digital

Digital (40, 96, 152)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 34, 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, 62, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)

(40, 96, 273)-Net over F₂₇ — Digital

Digital (40, 96, 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, 96, 370)-Net in Base 27 — Constructive

(40, 96, 370)-net in base 27, using

base change [i] based on digital (16, 72, 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]

(40, 96, 35106)-Net in Base 27 — Upper bound on s

There is no (40, 96, 35107)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 257741 675806 404035 734391 103020 921918 095374 182685 707125 705192 304558 383256 204632 169660 561458 451666 391494 358350 454025 512899 306651 852826 377865 > 27⁹⁶ [i]