MinT - Best Known (159, 159+73, s)-Nets in Base 3

Best Known (159, 159+73, s)-Nets in Base 3

(159, 159+73, 192)-Net over F₃ — Constructive and digital

Digital (159, 232, 192)-net over F₃, using

3¹ times duplication [i] based on digital (158, 231, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 77, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(159, 159+73, 434)-Net over F₃ — Digital

Digital (159, 232, 434)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+73, 8191)-Net in Base 3 — Upper bound on s

There is no (159, 232, 8192)-net in base 3, because

1 times m-reduction [i] would yield (159, 231, 8192)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 462721 552572 448781 236776 102242 471673 001882 635562 442014 712095 272459 390306 275746 849342 761825 367995 837636 870145 > 3²³¹ [i]