MinT - Best Known (124−62, 124, s)-Nets in Base 5

Best Known (124−62, 124, s)-Nets in Base 5

(124−62, 124, 82)-Net over F₅ — Constructive and digital

Digital (62, 124, 82)-net over F₅, using

t-expansion [i] based on digital (48, 124, 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]

(124−62, 124, 124)-Net over F₅ — Digital

Digital (62, 124, 124)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−62, 124, 1917)-Net in Base 5 — Upper bound on s

There is no (62, 124, 1918)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 473 409323 684415 705087 443221 463235 203009 894093 262879 711095 600908 857774 859279 191543 826969 > 5¹²⁴ [i]