MinT - Best Known (52, 52+41, s)-Nets in Base 4

Best Known (52, 52+41, s)-Nets in Base 4

(52, 52+41, 98)-Net over F₄ — Constructive and digital

Digital (52, 93, 98)-net over F₄, using

1 times m-reduction [i] based on digital (52, 94, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 47, 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]

(52, 52+41, 113)-Net over F₄ — Digital

Digital (52, 93, 113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+41, 1611)-Net in Base 4 — Upper bound on s

There is no (52, 93, 1612)-net in base 4, because

1 times m-reduction [i] would yield (52, 92, 1612)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24 544159 722572 123936 845080 409624 662565 066089 905032 511896 > 4⁹² [i]