MinT - Best Known (54, 54+53, s)-Nets in Base 5

Best Known (54, 54+53, s)-Nets in Base 5

(54, 54+53, 82)-Net over F₅ — Constructive and digital

Digital (54, 107, 82)-net over F₅, using

t-expansion [i] based on digital (48, 107, 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+53, 114)-Net over F₅ — Digital

Digital (54, 107, 114)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+53, 1846)-Net in Base 5 — Upper bound on s

There is no (54, 107, 1847)-net in base 5, because

1 times m-reduction [i] would yield (54, 106, 1847)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123 374351 673269 389934 446998 452586 022242 873281 669004 181456 575719 137881 568153 > 5¹⁰⁶ [i]