MinT - Best Known (15, 15+38, s)-Nets in Base 5

Best Known (15, 15+38, s)-Nets in Base 5

(15, 15+38, 36)-Net over F₅ — Constructive and digital

Digital (15, 53, 36)-net over F₅, using

net from sequence [i] based on digital (15, 35)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 11, N(F)Â =Â 32, and 4 places with degree 2 [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

(15, 15+38, 39)-Net over F₅ — Digital

Digital (15, 53, 39)-net over F₅, using

t-expansion [i] based on digital (14, 53, 39)-net over F₅, using
- net from sequence [i] based on digital (14, 38)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 14 and N(F) ≥ 39, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(15, 15+38, 162)-Net in Base 5 — Upper bound on s

There is no (15, 53, 163)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵³, 163, S₅, 38), but
- the linear programming bound shows that MÂ â‰¥ 4136 952007 035305 632138 883691 790616 889219 074384 945301 394594 707744 545303 285121 917724 609375 / 360 510811 697524 902708 831132 056182 094445 736159 819828 > 5⁵³ [i]