MinT - Best Known (39, 39+68, s)-Nets in Base 5

Best Known (39, 39+68, s)-Nets in Base 5

(39, 39+68, 78)-Net over F₅ — Constructive and digital

Digital (39, 107, 78)-net over F₅, using

t-expansion [i] based on digital (38, 107, 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]

(39, 39+68, 511)-Net in Base 5 — Upper bound on s

There is no (39, 107, 512)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 642 397174 596036 230711 127030 851138 492968 255052 877948 401569 176495 455935 668225 > 5¹⁰⁷ [i]