MinT - Best Known (52, 52+51, s)-Nets in Base 5

Best Known (52, 52+51, s)-Nets in Base 5

(52, 52+51, 82)-Net over F₅ — Constructive and digital

Digital (52, 103, 82)-net over F₅, using

t-expansion [i] based on digital (48, 103, 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]

(52, 52+51, 110)-Net over F₅ — Digital

Digital (52, 103, 110)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+51, 1790)-Net in Base 5 — Upper bound on s

There is no (52, 103, 1791)-net in base 5, because

1 times m-reduction [i] would yield (52, 102, 1791)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 198574 455301 143331 601223 537232 409443 170181 742065 888597 658844 724717 493149 > 5¹⁰² [i]