MinT - Best Known (75−54, 75, s)-Nets in Base 5

Best Known (75−54, 75, s)-Nets in Base 5

(75−54, 75, 43)-Net over F₅ — Constructive and digital

Digital (21, 75, 43)-net over F₅, using

t-expansion [i] based on digital (18, 75, 43)-net over F₅, using
- net from sequence [i] based on digital (18, 42)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 17, N(F)Â =Â 42, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(75−54, 75, 50)-Net over F₅ — Digital

Digital (21, 75, 50)-net over F₅, using

net from sequence [i] based on digital (21, 49)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 21 and N(F) ≥ 50, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(75−54, 75, 219)-Net in Base 5 — Upper bound on s

There is no (21, 75, 220)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 27832 147160 210266 466046 383992 665668 114669 466889 071217 > 5⁷⁵ [i]