MinT - Best Known (162, 162+62, s)-Nets in Base 4

Best Known (162, 162+62, s)-Nets in Base 4

(162, 162+62, 531)-Net over F₄ — Constructive and digital

Digital (162, 224, 531)-net over F₄, using

t-expansion [i] based on digital (161, 224, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 77, 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]

(162, 162+62, 1292)-Net over F₄ — Digital

Digital (162, 224, 1292)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+62, 92717)-Net in Base 4 — Upper bound on s

There is no (162, 224, 92718)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726 943191 680596 390678 002393 615582 638259 467346 835929 236554 920624 770259 446927 688363 201303 517275 502575 756313 136182 491322 000426 345808 221360 > 4²²⁴ [i]