MinT - Best Known (25, 25+86, s)-Nets in Base 5

Best Known (25, 25+86, s)-Nets in Base 5

(25, 25+86, 51)-Net over F₅ — Constructive and digital

Digital (25, 111, 51)-net over F₅, using

t-expansion [i] based on digital (22, 111, 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+86, 55)-Net over F₅ — Digital

Digital (25, 111, 55)-net over F₅, using

t-expansion [i] based on digital (23, 111, 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+86, 131)-Net in Base 5 — Upper bound on s

There is no (25, 111, 132)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹¹, 132, S₅, 86), but
- the linear programming bound shows that MÂ â‰¥ 1328 728470 029748 307471 104736 168611 135324 328576 524347 163279 049510 720142 279751 598834 991455 078125 / 2750 177817 872749 > 5¹¹¹ [i]