MinT - Best Known (39, 39+36, s)-Nets in Base 5

Best Known (39, 39+36, s)-Nets in Base 5

(39, 39+36, 78)-Net over F₅ — Constructive and digital

Digital (39, 75, 78)-net over F₅, using

t-expansion [i] based on digital (38, 75, 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+36, 96)-Net over F₅ — Digital

Digital (39, 75, 96)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+36, 1530)-Net in Base 5 — Upper bound on s

There is no (39, 75, 1531)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 26680 258537 282042 157956 488702 692702 813107 004209 351225 > 5⁷⁵ [i]