MinT - Best Known (149, 149+61, s)-Nets in Base 4

Best Known (149, 149+61, s)-Nets in Base 4

(149, 149+61, 531)-Net over F₄ — Constructive and digital

Digital (149, 210, 531)-net over F₄, using

3 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 71, 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]

(149, 149+61, 990)-Net over F₄ — Digital

Digital (149, 210, 990)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+61, 62784)-Net in Base 4 — Upper bound on s

There is no (149, 210, 62785)-net in base 4, because

1 times m-reduction [i] would yield (149, 209, 62785)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677231 094367 049536 304374 308450 543271 831066 662828 287279 128554 520854 413056 352071 270006 489887 046082 724714 540360 654232 930762 806304 > 4²⁰⁹ [i]