MinT - Best Known (39, 39+46, s)-Nets in Base 27

Best Known (39, 39+46, s)-Nets in Base 27

(39, 39+46, 170)-Net over F₂₇ — Constructive and digital

Digital (39, 85, 170)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 30, 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 (9, 55, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(39, 39+46, 341)-Net over F₂₇ — Digital

Digital (39, 85, 341)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+46, 370)-Net in Base 27 — Constructive

(39, 85, 370)-net in base 27, using

7 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+46, 70669)-Net in Base 27 — Upper bound on s

There is no (39, 85, 70670)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 342481 744752 445129 065147 047783 410381 874849 753152 587537 097328 881841 305861 246714 773480 466258 674342 193430 062231 048099 529897 > 27⁸⁵ [i]