MinT - Best Known (38, 86, s)-Nets in Base 27

Best Known (38, 86, s)-Nets in Base 27

(38, 86, 164)-Net over F₂₇ — Constructive and digital

Digital (38, 86, 164)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 31, 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]
2. digital (7, 55, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)

(38, 86, 288)-Net over F₂₇ — Digital

Digital (38, 86, 288)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 86, 370)-Net in Base 27 — Constructive

(38, 86, 370)-net in base 27, using

2 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 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]

(38, 86, 50738)-Net in Base 27 — Upper bound on s

There is no (38, 86, 50739)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1251 445456 760287 953806 347645 964608 690333 841411 193020 832225 027620 246817 246630 672989 715713 626606 277087 214820 668882 786142 016913 > 27⁸⁶ [i]