MinT - Best Known (45−17, 45, s)-Nets in Base 4

Best Known (45−17, 45, s)-Nets in Base 4

(45−17, 45, 98)-Net over F₄ — Constructive and digital

Digital (28, 45, 98)-net over F₄, using

1 times m-reduction [i] based on digital (28, 46, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 23, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(45−17, 45, 116)-Net over F₄ — Digital

Digital (28, 45, 116)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(45−17, 45, 2563)-Net in Base 4 — Upper bound on s

There is no (28, 45, 2564)-net in base 4, because

1 times m-reduction [i] would yield (28, 44, 2564)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 309 836009 889448 696207 906240 > 4⁴⁴ [i]