MinT - Best Known (15, 15+37, s)-Nets in Base 5

Best Known (15, 15+37, s)-Nets in Base 5

(15, 15+37, 36)-Net over F₅ — Constructive and digital

Digital (15, 52, 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+37, 39)-Net over F₅ — Digital

Digital (15, 52, 39)-net over F₅, using

t-expansion [i] based on digital (14, 52, 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+37, 167)-Net in Base 5 — Upper bound on s

There is no (15, 52, 168)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵², 168, S₅, 37), but
- the linear programming bound shows that MÂ â‰¥ 347 703493 821347 666054 839450 253497 835097 802322 624269 021677 045913 065740 023739 635944 366455 078125 / 141 997676 783544 632149 282153 069793 812520 701866 031308 159181 > 5⁵² [i]