MinT - Best Known (137, 137+57, s)-Nets in Base 4

Best Known (137, 137+57, s)-Nets in Base 4

(137, 137+57, 531)-Net over F₄ — Constructive and digital

Digital (137, 194, 531)-net over F₄, using

1 times m-reduction [i] based on digital (137, 195, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 65, 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]

(137, 137+57, 883)-Net over F₄ — Digital

Digital (137, 194, 883)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+57, 53163)-Net in Base 4 — Upper bound on s

There is no (137, 194, 53164)-net in base 4, because

1 times m-reduction [i] would yield (137, 193, 53164)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 157 677307 321606 607390 195797 335768 540681 764278 144545 744665 871235 491941 296417 832145 315593 689341 186803 950375 367784 509944 > 4¹⁹³ [i]