MinT - Best Known (109, 109+43, s)-Nets in Base 4

Best Known (109, 109+43, s)-Nets in Base 4

(109, 109+43, 531)-Net over F₄ — Constructive and digital

Digital (109, 152, 531)-net over F₄, using

1 times m-reduction [i] based on digital (109, 153, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 51, 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]

(109, 109+43, 852)-Net over F₄ — Digital

Digital (109, 152, 852)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+43, 61709)-Net in Base 4 — Upper bound on s

There is no (109, 152, 61710)-net in base 4, because

1 times m-reduction [i] would yield (109, 151, 61710)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 150434 213871 223129 199837 737388 189131 072608 735275 019834 989306 426994 427763 246639 359978 672784 > 4¹⁵¹ [i]