MinT - Best Known (231−63, 231, s)-Nets in Base 3

Best Known (231−63, 231, s)-Nets in Base 3

(231−63, 231, 288)-Net over F₃ — Constructive and digital

Digital (168, 231, 288)-net over F₃, using

t-expansion [i] based on digital (167, 231, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (167, 234, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 78, 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]

(231−63, 231, 692)-Net over F₃ — Digital

Digital (168, 231, 692)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−63, 231, 21494)-Net in Base 3 — Upper bound on s

There is no (168, 231, 21495)-net in base 3, because

1 times m-reduction [i] would yield (168, 230, 21495)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 757990 606089 985408 614894 098869 509525 958200 999269 344027 491111 676221 643335 745188 954201 990204 364968 156976 749219 > 3²³⁰ [i]