MinT - Best Known (42−28, 42, s)-Nets in Base 27

Best Known (42−28, 42, s)-Nets in Base 27

(42−28, 42, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 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]

(42−28, 42, 116)-Net in Base 27 — Constructive

(14, 42, 116)-net in base 27, using

6 times m-reduction [i] based on (14, 48, 116)-net in base 27, using
- base change [i] based on digital (2, 36, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(42−28, 42, 136)-Net over F₂₇ — Digital

Digital (14, 42, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 42, 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]

(42−28, 42, 4569)-Net in Base 27 — Upper bound on s

There is no (14, 42, 4570)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 310385 183513 233211 286867 035489 327294 878019 993688 330036 240989 > 27⁴² [i]