MinT - Best Known (167−49, 167, s)-Nets in Base 4

Best Known (167−49, 167, s)-Nets in Base 4

(167−49, 167, 384)-Net over F₄ — Constructive and digital

Digital (118, 167, 384)-net over F₄, using

t-expansion [i] based on digital (117, 167, 384)-net over F₄, using
- 1 times m-reduction [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]

(167−49, 167, 786)-Net over F₄ — Digital

Digital (118, 167, 786)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−49, 167, 47677)-Net in Base 4 — Upper bound on s

There is no (118, 167, 47678)-net in base 4, because

1 times m-reduction [i] would yield (118, 166, 47678)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8751 823927 464079 023941 283737 457046 446851 624421 324527 306508 188801 203674 218648 821883 845791 640832 798401 > 4¹⁶⁶ [i]