MinT - Best Known (58, 58+49, s)-Nets in Base 4

Best Known (58, 58+49, s)-Nets in Base 4

(58, 58+49, 90)-Net over F₄ — Constructive and digital

Digital (58, 107, 90)-net over F₄, using

1 times m-reduction [i] based on digital (58, 108, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 54, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(58, 58+49, 112)-Net over F₄ — Digital

Digital (58, 107, 112)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+49, 1471)-Net in Base 4 — Upper bound on s

There is no (58, 107, 1472)-net in base 4, because

1 times m-reduction [i] would yield (58, 106, 1472)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6675 444880 972270 347845 798891 653439 153108 987391 720130 908518 111509 > 4¹⁰⁶ [i]