MinT - Best Known (169−49, 169, s)-Nets in Base 4

Best Known (169−49, 169, s)-Nets in Base 4

(169−49, 169, 531)-Net over F₄ — Constructive and digital

Digital (120, 169, 531)-net over F₄, using

4¹ times duplication [i] based on digital (119, 168, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 56, 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]

(169−49, 169, 835)-Net over F₄ — Digital

Digital (120, 169, 835)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−49, 169, 53518)-Net in Base 4 — Upper bound on s

There is no (120, 169, 53519)-net in base 4, because

1 times m-reduction [i] would yield (120, 168, 53519)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140020 844660 016692 010285 176449 718457 977050 803952 216115 713534 768727 334391 117748 445825 829340 808826 236016 > 4¹⁶⁸ [i]