MinT - Best Known (12, 12+30, s)-Nets in Base 27

Best Known (12, 12+30, s)-Nets in Base 27

(12, 12+30, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 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]

(12, 12+30, 100)-Net in Base 27 — Constructive

(12, 42, 100)-net in base 27, using

2 times m-reduction [i] based on (12, 44, 100)-net in base 27, using
- base change [i] based on digital (1, 33, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(12, 12+30, 109)-Net over F₂₇ — Digital

Digital (12, 42, 109)-net over F₂₇, using

net from sequence [i] based on digital (12, 108)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 12 and N(F) ≥ 109, using
  - a curve from the manYPoints database [i]

(12, 12+30, 2507)-Net in Base 27 — Upper bound on s

There is no (12, 42, 2508)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 311144 994895 872684 496503 402479 421484 276952 716264 188304 690865 > 27⁴² [i]