MinT - Best Known (89−41, 89, s)-Nets in Base 4

Best Known (89−41, 89, s)-Nets in Base 4

(89−41, 89, 76)-Net over F₄ — Constructive and digital

Digital (48, 89, 76)-net over F₄, using

1 times m-reduction [i] based on digital (48, 90, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 45, 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]

(89−41, 89, 95)-Net over F₄ — Digital

Digital (48, 89, 95)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−41, 89, 1217)-Net in Base 4 — Upper bound on s

There is no (48, 89, 1218)-net in base 4, because

1 times m-reduction [i] would yield (48, 88, 1218)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 96206 447042 419567 470250 027818 214550 599361 438036 308624 > 4⁸⁸ [i]