MinT - Best Known (89, 89+35, s)-Nets in Base 3

Best Known (89, 89+35, s)-Nets in Base 3

(89, 89+35, 228)-Net over F₃ — Constructive and digital

Digital (89, 124, 228)-net over F₃, using

3¹ times duplication [i] based on digital (88, 123, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 41, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(89, 89+35, 369)-Net over F₃ — Digital

Digital (89, 124, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+35, 10146)-Net in Base 3 — Upper bound on s

There is no (89, 124, 10147)-net in base 3, because

1 times m-reduction [i] would yield (89, 123, 10147)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48547 763301 772616 563398 664892 396261 233649 519216 892683 025831 > 3¹²³ [i]