MinT - Best Known (160−45, 160, s)-Nets in Base 3

Best Known (160−45, 160, s)-Nets in Base 3

(160−45, 160, 252)-Net over F₃ — Constructive and digital

Digital (115, 160, 252)-net over F₃, using

3¹ times duplication [i] based on digital (114, 159, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 53, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(160−45, 160, 456)-Net over F₃ — Digital

Digital (115, 160, 456)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−45, 160, 12687)-Net in Base 3 — Upper bound on s

There is no (115, 160, 12688)-net in base 3, because

1 times m-reduction [i] would yield (115, 159, 12688)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7289 674307 109847 511065 406589 955080 072795 384812 850901 249062 540881 696496 717153 > 3¹⁵⁹ [i]