MinT - Best Known (50, 50+98, s)-Nets in Base 5

Best Known (50, 50+98, s)-Nets in Base 5

(50, 50+98, 82)-Net over F₅ — Constructive and digital

Digital (50, 148, 82)-net over F₅, using

t-expansion [i] based on digital (48, 148, 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]

(50, 50+98, 96)-Net over F₅ — Digital

Digital (50, 148, 96)-net over F₅, using

t-expansion [i] based on digital (49, 148, 96)-net over F₅, using
- net from sequence [i] based on digital (49, 95)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 49 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(50, 50+98, 581)-Net in Base 5 — Upper bound on s

There is no (50, 148, 582)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 743686 286649 298695 696269 199233 893571 453729 419553 719736 755857 991164 662300 938516 849974 606595 221091 974425 > 5¹⁴⁸ [i]