MinT - Best Known (166−47, 166, s)-Nets in Base 4

Best Known (166−47, 166, s)-Nets in Base 4

(166−47, 166, 531)-Net over F₄ — Constructive and digital

Digital (119, 166, 531)-net over F₄, using

2 times m-reduction [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]

(166−47, 166, 915)-Net over F₄ — Digital

Digital (119, 166, 915)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−47, 166, 65514)-Net in Base 4 — Upper bound on s

There is no (119, 166, 65515)-net in base 4, because

1 times m-reduction [i] would yield (119, 165, 65515)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2187 645143 622578 102407 630930 297191 147079 669236 542562 454762 151982 909357 674735 595205 779699 976512 094336 > 4¹⁶⁵ [i]