MinT - Best Known (45−21, 45, s)-Nets in Base 4

Best Known (45−21, 45, s)-Nets in Base 4

(45−21, 45, 48)-Net over F₄ — Constructive and digital

Digital (24, 45, 48)-net over F₄, using

1 times m-reduction [i] based on digital (24, 46, 48)-net over F₄, using
- trace code for nets [i] based on digital (1, 23, 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]

(45−21, 45, 57)-Net over F₄ — Digital

Digital (24, 45, 57)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(45−21, 45, 665)-Net in Base 4 — Upper bound on s

There is no (24, 45, 666)-net in base 4, because

1 times m-reduction [i] would yield (24, 44, 666)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 313 866455 558385 684712 263760 > 4⁴⁴ [i]