MinT - Best Known (59, 59+86, s)-Nets in Base 5

Best Known (59, 59+86, s)-Nets in Base 5

(59, 59+86, 82)-Net over F₅ — Constructive and digital

Digital (59, 145, 82)-net over F₅, using

t-expansion [i] based on digital (48, 145, 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]

(59, 59+86, 112)-Net over F₅ — Digital

Digital (59, 145, 112)-net over F₅, using

t-expansion [i] based on digital (57, 145, 112)-net over F₅, using
- net from sequence [i] based on digital (57, 111)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 57 and N(F) ≥ 112, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(59, 59+86, 928)-Net in Base 5 — Upper bound on s

There is no (59, 145, 929)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 225178 553893 163550 344747 793693 307225 781435 895539 423669 290959 408806 511300 175682 912447 602928 891955 549405 > 5¹⁴⁵ [i]