MinT - Best Known (92−41, 92, s)-Nets in Base 4

Best Known (92−41, 92, s)-Nets in Base 4

(92−41, 92, 98)-Net over F₄ — Constructive and digital

Digital (51, 92, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 46, 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]

(92−41, 92, 108)-Net over F₄ — Digital

Digital (51, 92, 108)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−41, 92, 1502)-Net in Base 4 — Upper bound on s

There is no (51, 92, 1503)-net in base 4, because

1 times m-reduction [i] would yield (51, 91, 1503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 138052 406111 284341 493510 862747 753618 069636 394297 634291 > 4⁹¹ [i]