MinT - Best Known (170−45, 170, s)-Nets in Base 3

Best Known (170−45, 170, s)-Nets in Base 3

(170−45, 170, 288)-Net over F₃ — Constructive and digital

Digital (125, 170, 288)-net over F₃, using

1 times m-reduction [i] based on digital (125, 171, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 57, 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]

(170−45, 170, 598)-Net over F₃ — Digital

Digital (125, 170, 598)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−45, 170, 20918)-Net in Base 3 — Upper bound on s

There is no (125, 170, 20919)-net in base 3, because

1 times m-reduction [i] would yield (125, 169, 20919)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 134363 109304 645297 282987 134790 770141 094328 206266 318254 398598 238396 888334 367621 > 3¹⁶⁹ [i]