MinT - Best Known (146, 146+57, s)-Nets in Base 4

Best Known (146, 146+57, s)-Nets in Base 4

(146, 146+57, 531)-Net over F₄ — Constructive and digital

Digital (146, 203, 531)-net over F₄, using

t-expansion [i] based on digital (145, 203, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 69, 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]

(146, 146+57, 1116)-Net over F₄ — Digital

Digital (146, 203, 1116)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+57, 83022)-Net in Base 4 — Upper bound on s

There is no (146, 203, 83023)-net in base 4, because

1 times m-reduction [i] would yield (146, 202, 83023)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 319369 348286 647390 224733 040737 002171 432996 440266 028818 448120 330022 295023 857044 577519 703619 869494 205448 833480 859125 978140 > 4²⁰² [i]