MinT - Best Known (42−26, 42, s)-Nets in Base 27

Best Known (42−26, 42, s)-Nets in Base 27

(42−26, 42, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 42, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 42, 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]

(42−26, 42, 144)-Net over F₂₇ — Digital

Digital (16, 42, 144)-net over F₂₇, using

net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(42−26, 42, 160)-Net in Base 27 — Constructive

(16, 42, 160)-net in base 27, using

2 times m-reduction [i] based on (16, 44, 160)-net in base 27, using
- base change [i] based on digital (5, 33, 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]

(42−26, 42, 167)-Net in Base 27

(16, 42, 167)-net in base 27, using

2 times m-reduction [i] based on (16, 44, 167)-net in base 27, using
- base change [i] based on digital (5, 33, 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]

(42−26, 42, 9173)-Net in Base 27 — Upper bound on s

There is no (16, 42, 9174)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 311097 182002 412632 844468 358346 026855 892240 325166 119689 319813 > 27⁴² [i]