MinT - Best Known (49, 49+42, s)-Nets in Base 4

Best Known (49, 49+42, s)-Nets in Base 4

(49, 49+42, 76)-Net over F₄ — Constructive and digital

Digital (49, 91, 76)-net over F₄, using

1 times m-reduction [i] based on digital (49, 92, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 46, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(49, 49+42, 96)-Net over F₄ — Digital

Digital (49, 91, 96)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+42, 1158)-Net in Base 4 — Upper bound on s

There is no (49, 91, 1159)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 152125 148265 997849 743971 733512 337830 809316 473316 016592 > 4⁹¹ [i]