MinT - Best Known (47, 86, s)-Nets in Base 27

Best Known (47, 86, s)-Nets in Base 27

(47, 86, 210)-Net over F₂₇ — Constructive and digital

Digital (47, 86, 210)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 17, 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, 23, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
3. digital (7, 46, 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]

(47, 86, 370)-Net in Base 27 — Constructive

(47, 86, 370)-net in base 27, using

t-expansion [i] based on (43, 86, 370)-net in base 27, using
- 22 times m-reduction [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]

(47, 86, 1022)-Net over F₂₇ — Digital

Digital (47, 86, 1022)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 86, 772157)-Net in Base 27 — Upper bound on s

There is no (47, 86, 772158)-net in base 27, because

1 times m-reduction [i] would yield (47, 85, 772158)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 336188 592081 347806 891777 636077 204012 915849 335622 406908 464930 538301 247861 840989 159737 908237 998900 112823 913238 015269 388465 > 27⁸⁵ [i]