MinT - Best Known (44, 44+28, s)-Nets in Base 27

Best Known (44, 44+28, s)-Nets in Base 27

(44, 44+28, 246)-Net over F₂₇ — Constructive and digital

Digital (44, 72, 246)-net over F₂₇, using

1 times m-reduction [i] based on digital (44, 73, 246)-net over F₂₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 16, 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, 21, 82)-net over F₂₇, using
    - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)
  3. digital (7, 36, 82)-net over F₂₇, using
    - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)

(44, 44+28, 370)-Net in Base 27 — Constructive

(44, 72, 370)-net in base 27, using

t-expansion [i] based on (43, 72, 370)-net in base 27, using
- 36 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]

(44, 44+28, 2770)-Net over F₂₇ — Digital

Digital (44, 72, 2770)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+28, 5342975)-Net in Base 27 — Upper bound on s

There is no (44, 72, 5342976)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11 433828 044513 924999 575701 765566 035263 662899 391784 990967 961459 522821 988966 078915 833051 890941 676232 432129 > 27⁷² [i]