MinT - Best Known (58, 58+53, s)-Nets in Base 5

Best Known (58, 58+53, s)-Nets in Base 5

(58, 58+53, 82)-Net over F₅ — Constructive and digital

Digital (58, 111, 82)-net over F₅, using

t-expansion [i] based on digital (48, 111, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(58, 58+53, 132)-Net over F₅ — Digital

Digital (58, 111, 132)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+53, 2371)-Net in Base 5 — Upper bound on s

There is no (58, 111, 2372)-net in base 5, because

1 times m-reduction [i] would yield (58, 110, 2372)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77759 698199 197811 057373 730329 060565 092853 923415 497306 867209 341585 753671 215809 > 5¹¹⁰ [i]