MinT - Best Known (56−32, 56, s)-Nets in Base 5

Best Known (56−32, 56, s)-Nets in Base 5

(56−32, 56, 51)-Net over F₅ — Constructive and digital

Digital (24, 56, 51)-net over F₅, using

t-expansion [i] based on digital (22, 56, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(56−32, 56, 55)-Net over F₅ — Digital

Digital (24, 56, 55)-net over F₅, using

t-expansion [i] based on digital (23, 56, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(56−32, 56, 463)-Net in Base 5 — Upper bound on s

There is no (24, 56, 464)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1397 287415 094156 559345 561065 749900 324865 > 5⁵⁶ [i]