MinT - Best Known (39, 96, s)-Nets in Base 27

Best Known (39, 96, s)-Nets in Base 27

(39, 96, 146)-Net over F₂₇ — Constructive and digital

Digital (39, 96, 146)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (4, 32, 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 (7, 64, 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, 96, 224)-Net in Base 27 — Constructive

(39, 96, 224)-net in base 27, using

8 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(39, 96, 271)-Net over F₂₇ — Digital

Digital (39, 96, 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, 96, 298)-Net in Base 27

(39, 96, 298)-net in base 27, using

12 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F₈₁, using
  - net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
      - a curve from the manYPoints database [i]

(39, 96, 31206)-Net in Base 27 — Upper bound on s

There is no (39, 96, 31207)-net in base 27, because

1 times m-reduction [i] would yield (39, 95, 31207)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9546 577197 129298 548205 390194 434027 399289 092454 139908 857038 093104 934757 029320 606346 170567 162921 126889 242384 597032 413279 733456 140420 144425 > 27⁹⁵ [i]