MinT - Best Known (159−45, 159, s)-Nets in Base 4

Best Known (159−45, 159, s)-Nets in Base 4

(159−45, 159, 531)-Net over F₄ — Constructive and digital

Digital (114, 159, 531)-net over F₄, using

t-expansion [i] based on digital (113, 159, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 53, 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]

(159−45, 159, 884)-Net over F₄ — Digital

Digital (114, 159, 884)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−45, 159, 63605)-Net in Base 4 — Upper bound on s

There is no (114, 159, 63606)-net in base 4, because

1 times m-reduction [i] would yield (114, 158, 63606)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133517 139966 402832 682291 727636 918640 308668 588118 318845 336280 157251 021227 539177 837315 934461 228504 > 4¹⁵⁸ [i]