MinT - Best Known (54, 54+50, s)-Nets in Base 5

Best Known (54, 54+50, s)-Nets in Base 5

(54, 54+50, 82)-Net over F₅ — Constructive and digital

Digital (54, 104, 82)-net over F₅, using

t-expansion [i] based on digital (48, 104, 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]

(54, 54+50, 123)-Net over F₅ — Digital

Digital (54, 104, 123)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+50, 2039)-Net in Base 5 — Upper bound on s

There is no (54, 104, 2040)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 988863 491064 296985 703933 599422 951741 331804 800585 657641 577053 884593 774049 > 5¹⁰⁴ [i]