MinT - Best Known (172−72, 172, s)-Nets in Base 8

Best Known (172−72, 172, s)-Nets in Base 8

(172−72, 172, 354)-Net over F₈ — Constructive and digital

Digital (100, 172, 354)-net over F₈, using

t-expansion [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]

(172−72, 172, 582)-Net over F₈ — Digital

Digital (100, 172, 582)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−72, 172, 42089)-Net in Base 8 — Upper bound on s

There is no (100, 172, 42090)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214705 322000 415559 870461 789940 300194 459435 882686 188641 904689 748628 448265 631147 752277 926715 757494 810369 778939 049414 952665 203184 583282 980752 635798 674560 837018 > 8¹⁷² [i]