MinT - Best Known (74−35, 74, s)-Nets in Base 5

Best Known (74−35, 74, s)-Nets in Base 5

(74−35, 74, 78)-Net over F₅ — Constructive and digital

Digital (39, 74, 78)-net over F₅, using

t-expansion [i] based on digital (38, 74, 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]

(74−35, 74, 100)-Net over F₅ — Digital

Digital (39, 74, 100)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−35, 74, 1788)-Net in Base 5 — Upper bound on s

There is no (39, 74, 1789)-net in base 5, because

1 times m-reduction [i] would yield (39, 73, 1789)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1068 035313 526336 952198 413495 005173 285981 766505 368245 > 5⁷³ [i]