MinT - Best Known (158, 158+65, s)-Nets in Base 4

Best Known (158, 158+65, s)-Nets in Base 4

(158, 158+65, 531)-Net over F₄ — Constructive and digital

Digital (158, 223, 531)-net over F₄, using

t-expansion [i] based on digital (157, 223, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 75, 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]

(158, 158+65, 1027)-Net over F₄ — Digital

Digital (158, 223, 1027)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+65, 64028)-Net in Base 4 — Upper bound on s

There is no (158, 223, 64029)-net in base 4, because

1 times m-reduction [i] would yield (158, 222, 64029)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 440260 252076 668269 084115 237287 320773 918942 854748 226468 434515 824366 025989 971683 388939 372902 985104 910009 817685 656013 804665 086549 274320 > 4²²² [i]