MinT - Best Known (85−40, 85, s)-Nets in Base 5

Best Known (85−40, 85, s)-Nets in Base 5

(85−40, 85, 78)-Net over F₅ — Constructive and digital

Digital (45, 85, 78)-net over F₅, using

t-expansion [i] based on digital (38, 85, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(85−40, 85, 113)-Net over F₅ — Digital

Digital (45, 85, 113)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−40, 85, 1925)-Net in Base 5 — Upper bound on s

There is no (45, 85, 1926)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 258924 692663 526792 175915 491800 364656 063705 072854 612304 779585 > 5⁸⁵ [i]