MinT - Best Known (87, 124, s)-Nets in Base 3

Best Known (87, 124, s)-Nets in Base 3

(87, 124, 192)-Net over F₃ — Constructive and digital

Digital (87, 124, 192)-net over F₃, using

3¹ times duplication [i] based on digital (86, 123, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 41, 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]

(87, 124, 303)-Net over F₃ — Digital

Digital (87, 124, 303)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 124, 6859)-Net in Base 3 — Upper bound on s

There is no (87, 124, 6860)-net in base 3, because

1 times m-reduction [i] would yield (87, 123, 6860)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48520 863926 799352 543187 695840 567713 692193 063164 186857 604841 > 3¹²³ [i]