MinT - Best Known (35, 92, s)-Nets in Base 27

Best Known (35, 92, s)-Nets in Base 27

(35, 92, 116)-Net over F₂₇ — Constructive and digital

Digital (35, 92, 116)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (3, 31, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]
2. digital (4, 61, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(35, 92, 172)-Net in Base 27 — Constructive

(35, 92, 172)-net in base 27, using

t-expansion [i] based on (34, 92, 172)-net in base 27, using
- 16 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
  - base change [i] based on digital (7, 81, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(35, 92, 220)-Net over F₂₇ — Digital

Digital (35, 92, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 92, 220)-net over F₂₇, using
- net from sequence [i] based on digital (33, 219)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 33 and N(F) ≥ 220, using
    - Drinfeld modules of rank 1 [i]

(35, 92, 298)-Net in Base 27

(35, 92, 298)-net in base 27, using

base change [i] based on digital (12, 69, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(35, 92, 19482)-Net in Base 27 — Upper bound on s

There is no (35, 92, 19483)-net in base 27, because

1 times m-reduction [i] would yield (35, 91, 19483)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 17970 881580 973764 834872 170533 070414 645592 712833 347119 265649 110813 326943 646107 431377 691222 381917 138879 011806 160569 862671 508645 281033 > 27⁹¹ [i]