MinT - Best Known (142−41, 142, s)-Nets in Base 4

Best Known (142−41, 142, s)-Nets in Base 4

(142−41, 142, 384)-Net over F₄ — Constructive and digital

Digital (101, 142, 384)-net over F₄, using

2 times m-reduction [i] based on digital (101, 144, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 48, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(142−41, 142, 741)-Net over F₄ — Digital

Digital (101, 142, 741)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−41, 142, 48591)-Net in Base 4 — Upper bound on s

There is no (101, 142, 48592)-net in base 4, because

1 times m-reduction [i] would yield (101, 141, 48592)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 771143 555911 582267 222741 402003 182599 456570 856266 824435 956166 027207 820757 491543 355564 > 4¹⁴¹ [i]