MinT - Best Known (117, 160, s)-Nets in Base 4

Best Known (117, 160, s)-Nets in Base 4

(117, 160, 531)-Net over F₄ — Constructive and digital

Digital (117, 160, 531)-net over F₄, using

5 times m-reduction [i] based on digital (117, 165, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 55, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(117, 160, 1103)-Net over F₄ — Digital

Digital (117, 160, 1103)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 160, 104653)-Net in Base 4 — Upper bound on s

There is no (117, 160, 104654)-net in base 4, because

1 times m-reduction [i] would yield (117, 159, 104654)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534018 354722 962171 661153 906938 566632 154526 482721 367160 803366 519604 969002 845389 687799 946827 265548 > 4¹⁵⁹ [i]