MinT - Best Known (25, 25+68, s)-Nets in Base 5

Best Known (25, 25+68, s)-Nets in Base 5

(25, 25+68, 51)-Net over F₅ — Constructive and digital

Digital (25, 93, 51)-net over F₅, using

t-expansion [i] based on digital (22, 93, 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]

(25, 25+68, 55)-Net over F₅ — Digital

Digital (25, 93, 55)-net over F₅, using

t-expansion [i] based on digital (23, 93, 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]

(25, 25+68, 252)-Net in Base 5 — Upper bound on s

There is no (25, 93, 253)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 113847 437932 490574 804870 109869 893827 872248 316141 613685 110592 073625 > 5⁹³ [i]