MinT - Best Known (94−53, 94, s)-Nets in Base 27

Best Known (94−53, 94, s)-Nets in Base 27

(94−53, 94, 166)-Net over F₂₇ — Constructive and digital

Digital (41, 94, 166)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 33, 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 (8, 61, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(94−53, 94, 292)-Net over F₂₇ — Digital

Digital (41, 94, 292)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−53, 94, 370)-Net in Base 27 — Constructive

(41, 94, 370)-net in base 27, using

6 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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]

(94−53, 94, 53467)-Net in Base 27 — Upper bound on s

There is no (41, 94, 53468)-net in base 27, because

1 times m-reduction [i] would yield (41, 93, 53468)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 13 091244 194901 744224 107517 952792 787991 996301 035235 522687 021937 773799 503727 522190 132870 237971 318835 442146 640843 175866 866421 629330 991945 > 27⁹³ [i]