MinT - Best Known (115, 162, s)-Nets in Base 4

Best Known (115, 162, s)-Nets in Base 4

(115, 162, 531)-Net over F₄ — Constructive and digital

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]

(115, 162, 805)-Net over F₄ — Digital

Digital (115, 162, 805)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 162, 51475)-Net in Base 4 — Upper bound on s

There is no (115, 162, 51476)-net in base 4, because

1 times m-reduction [i] would yield (115, 161, 51476)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 547236 128753 705929 797000 786081 954468 936943 472942 941887 459478 634827 919014 754640 642517 779579 287744 > 4¹⁶¹ [i]