MinT - Best Known (169−51, 169, s)-Nets in Base 4

Best Known (169−51, 169, s)-Nets in Base 4

(169−51, 169, 384)-Net over F₄ — Constructive and digital

Digital (118, 169, 384)-net over F₄, using

4¹ times duplication [i] based on digital (117, 168, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 56, 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]

(169−51, 169, 704)-Net over F₄ — Digital

Digital (118, 169, 704)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−51, 169, 37680)-Net in Base 4 — Upper bound on s

There is no (118, 169, 37681)-net in base 4, because

1 times m-reduction [i] would yield (118, 168, 37681)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140056 159190 625490 779600 691317 324949 322026 481351 459008 006009 498370 240974 911834 134498 928743 304180 477520 > 4¹⁶⁸ [i]