MinT - Best Known (87, 87+62, s)-Nets in Base 8

Best Known (87, 87+62, s)-Nets in Base 8

(87, 87+62, 354)-Net over F₈ — Constructive and digital

Digital (87, 149, 354)-net over F₈, using

11 times m-reduction [i] based on digital (87, 160, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 80, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(87, 87+62, 529)-Net over F₈ — Digital

Digital (87, 149, 529)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+62, 38848)-Net in Base 8 — Upper bound on s

There is no (87, 149, 38849)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 515474 244185 623208 804849 281543 068558 910717 621820 997728 686805 402920 226077 884377 279394 107814 324031 615335 154343 507699 446665 614068 625856 > 8¹⁴⁹ [i]