MinT - Best Known (222−63, 222, s)-Nets in Base 3

Best Known (222−63, 222, s)-Nets in Base 3

(222−63, 222, 288)-Net over F₃ — Constructive and digital

Digital (159, 222, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 74, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(222−63, 222, 583)-Net over F₃ — Digital

Digital (159, 222, 583)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−63, 222, 15615)-Net in Base 3 — Upper bound on s

There is no (159, 222, 15616)-net in base 3, because

1 times m-reduction [i] would yield (159, 221, 15616)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2778 561922 979155 882359 807720 681278 687841 010630 392782 879547 709182 895910 921119 125935 836168 011534 749528 185857 > 3²²¹ [i]