MinT - Best Known (216−57, 216, s)-Nets in Base 3

Best Known (216−57, 216, s)-Nets in Base 3

(216−57, 216, 288)-Net over F₃ — Constructive and digital

Digital (159, 216, 288)-net over F₃, using

6 times m-reduction [i] based on 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]

(216−57, 216, 736)-Net over F₃ — Digital

Digital (159, 216, 736)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−57, 216, 26009)-Net in Base 3 — Upper bound on s

There is no (159, 216, 26010)-net in base 3, because

1 times m-reduction [i] would yield (159, 215, 26010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 814813 511481 256578 947494 502305 088284 792686 018591 837257 832581 280615 285423 738445 297397 261344 712155 470873 > 3²¹⁵ [i]