MinT - Best Known (163−47, 163, s)-Nets in Base 4

Best Known (163−47, 163, s)-Nets in Base 4

(163−47, 163, 531)-Net over F₄ — Constructive and digital

Digital (116, 163, 531)-net over F₄, using

4¹ times duplication [i] based on digital (115, 162, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 54, 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]

(163−47, 163, 831)-Net over F₄ — Digital

Digital (116, 163, 831)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−47, 163, 54674)-Net in Base 4 — Upper bound on s

There is no (116, 163, 54675)-net in base 4, because

1 times m-reduction [i] would yield (116, 162, 54675)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 185811 157517 830811 663927 880053 832271 390552 151238 742060 383504 366250 617084 574145 764767 559395 868416 > 4¹⁶² [i]