MinT - Best Known (42, 42+41, s)-Nets in Base 5

Best Known (42, 42+41, s)-Nets in Base 5

(42, 42+41, 78)-Net over F₅ — Constructive and digital

Digital (42, 83, 78)-net over F₅, using

t-expansion [i] based on digital (38, 83, 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]

(42, 42+41, 94)-Net over F₅ — Digital

Digital (42, 83, 94)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+41, 1509)-Net in Base 5 — Upper bound on s

There is no (42, 83, 1510)-net in base 5, because

1 times m-reduction [i] would yield (42, 82, 1510)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2076 543499 771965 860243 056397 165298 109914 468254 358396 105025 > 5⁸² [i]