MinT - Best Known (87, 87+35, s)-Nets in Base 3

Best Known (87, 87+35, s)-Nets in Base 3

(87, 87+35, 204)-Net over F₃ — Constructive and digital

Digital (87, 122, 204)-net over F₃, using

1 times m-reduction [i] based on digital (87, 123, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 41, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(87, 87+35, 343)-Net over F₃ — Digital

Digital (87, 122, 343)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+35, 8914)-Net in Base 3 — Upper bound on s

There is no (87, 122, 8915)-net in base 3, because

1 times m-reduction [i] would yield (87, 121, 8915)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5396 916693 139305 268409 044098 817763 931249 252162 530431 483911 > 3¹²¹ [i]