MinT - Best Known (97−54, 97, s)-Nets in Base 27

Best Known (97−54, 97, s)-Nets in Base 27

(97−54, 97, 170)-Net over F₂₇ — Constructive and digital

Digital (43, 97, 170)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 34, 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, 63, 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]

(97−54, 97, 321)-Net over F₂₇ — Digital

Digital (43, 97, 321)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−54, 97, 370)-Net in Base 27 — Constructive

(43, 97, 370)-net in base 27, using

11 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]

(97−54, 97, 58295)-Net in Base 27 — Upper bound on s

There is no (43, 97, 58296)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 956123 823942 025445 894377 632586 269494 283479 182346 197742 978997 288590 608390 166462 661356 994802 343147 580970 600924 445729 494759 611123 842439 885217 > 27⁹⁷ [i]