MinT - Best Known (217−55, 217, s)-Nets in Base 3

Best Known (217−55, 217, s)-Nets in Base 3

(217−55, 217, 288)-Net over F₃ — Constructive and digital

Digital (162, 217, 288)-net over F₃, using

t-expansion [i] based on digital (161, 217, 288)-net over F₃, using
- 8 times m-reduction [i] based on digital (161, 225, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 75, 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]

(217−55, 217, 861)-Net over F₃ — Digital

Digital (162, 217, 861)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−55, 217, 35811)-Net in Base 3 — Upper bound on s

There is no (162, 217, 35812)-net in base 3, because

1 times m-reduction [i] would yield (162, 216, 35812)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 435882 034737 323408 301757 443627 721459 597522 422688 558141 549656 202357 837286 692560 133143 136547 021903 602417 > 3²¹⁶ [i]