MinT - Best Known (87, 87+65, s)-Nets in Base 3

Best Known (87, 87+65, s)-Nets in Base 3

(87, 87+65, 80)-Net over F₃ — Constructive and digital

Digital (87, 152, 80)-net over F₃, using

6 times m-reduction [i] based on digital (87, 158, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 79, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(87, 87+65, 122)-Net over F₃ — Digital

Digital (87, 152, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+65, 1109)-Net in Base 3 — Upper bound on s

There is no (87, 152, 1110)-net in base 3, because

1 times m-reduction [i] would yield (87, 151, 1110)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 115991 540332 603561 238217 201361 778854 552110 022262 605996 171959 919108 711745 > 3¹⁵¹ [i]