MinT - Best Known (15, 15+41, s)-Nets in Base 5

Best Known (15, 15+41, s)-Nets in Base 5

(15, 15+41, 36)-Net over F₅ — Constructive and digital

Digital (15, 56, 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+41, 39)-Net over F₅ — Digital

Digital (15, 56, 39)-net over F₅, using

t-expansion [i] based on digital (14, 56, 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+41, 148)-Net in Base 5 — Upper bound on s

There is no (15, 56, 149)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁶, 149, S₅, 41), but
- the linear programming bound shows that MÂ â‰¥ 572 078975 469705 953424 623342 004460 721768 116576 630226 648774 807156 675041 078236 443513 596896 082162 857055 664062 500000 000000 / 388673 139085 638175 334731 197626 662833 952575 177980 704147 964287 113139 126680 294113 > 5⁵⁶ [i]