MinT - Best Known (18, 18+15, s)-Nets in Base 4

Best Known (18, 18+15, s)-Nets in Base 4

(18, 18+15, 48)-Net over F₄ — Constructive and digital

Digital (18, 33, 48)-net over F₄, using

1 times m-reduction [i] based on digital (18, 34, 48)-net over F₄, using
- trace code for nets [i] based on digital (1, 17, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]

(18, 18+15, 51)-Net over F₄ — Digital

Digital (18, 33, 51)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 18+15, 631)-Net in Base 4 — Upper bound on s

There is no (18, 33, 632)-net in base 4, because

1 times m-reduction [i] would yield (18, 32, 632)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18 531055 492803 460195 > 4³² [i]