MinT - Best Known (157−64, 157, s)-Nets in Base 8

Best Known (157−64, 157, s)-Nets in Base 8

(157−64, 157, 354)-Net over F₈ — Constructive and digital

Digital (93, 157, 354)-net over F₈, using

15 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 86, 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]

(157−64, 157, 608)-Net over F₈ — Digital

Digital (93, 157, 608)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−64, 157, 49248)-Net in Base 8 — Upper bound on s

There is no (93, 157, 49249)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6100 211562 988636 029300 993275 844731 260758 526299 569167 154284 034529 323160 821452 737699 715947 333744 623840 230101 579429 337260 377448 726690 411531 700207 > 8¹⁵⁷ [i]