MinT - Best Known (235−65, 235, s)-Nets in Base 4

Best Known (235−65, 235, s)-Nets in Base 4

(235−65, 235, 531)-Net over F₄ — Constructive and digital

Digital (170, 235, 531)-net over F₄, using

t-expansion [i] based on digital (169, 235, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 81, 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]

(235−65, 235, 1349)-Net over F₄ — Digital

Digital (170, 235, 1349)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−65, 235, 107700)-Net in Base 4 — Upper bound on s

There is no (170, 235, 107701)-net in base 4, because

1 times m-reduction [i] would yield (170, 234, 107701)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 282048 775495 190429 858573 644692 342656 516883 094538 811648 388073 629499 775803 681195 836042 530819 251583 613804 002700 798453 682011 131977 676970 947067 > 4²³⁴ [i]