MinT - Best Known (55, 55+53, s)-Nets in Base 5

Best Known (55, 55+53, s)-Nets in Base 5

(55, 55+53, 82)-Net over F₅ — Constructive and digital

Digital (55, 108, 82)-net over F₅, using

t-expansion [i] based on digital (48, 108, 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]

(55, 55+53, 118)-Net over F₅ — Digital

Digital (55, 108, 118)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+53, 1966)-Net in Base 5 — Upper bound on s

There is no (55, 108, 1967)-net in base 5, because

1 times m-reduction [i] would yield (55, 107, 1967)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 623 780139 491854 833319 633407 576130 918846 552350 004805 481075 223896 163217 755033 > 5¹⁰⁷ [i]