MinT - Best Known (34−20, 34, s)-Nets in Base 27

Best Known (34−20, 34, s)-Nets in Base 27

(34−20, 34, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 34, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 34, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(34−20, 34, 136)-Net over F₂₇ — Digital

Digital (14, 34, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 34, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(34−20, 34, 160)-Net in Base 27 — Constructive

(14, 34, 160)-net in base 27, using

2 times m-reduction [i] based on (14, 36, 160)-net in base 27, using
- base change [i] based on digital (5, 27, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(34−20, 34, 167)-Net in Base 27

(14, 34, 167)-net in base 27, using

2 times m-reduction [i] based on (14, 36, 167)-net in base 27, using
- base change [i] based on digital (5, 27, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(34−20, 34, 12807)-Net in Base 27 — Upper bound on s

There is no (14, 34, 12808)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4 639160 970782 095393 144813 336554 632173 969028 347953 > 27³⁴ [i]