MinT - Best Known (15, 15+54, s)-Nets in Base 5

Best Known (15, 15+54, s)-Nets in Base 5

(15, 15+54, 36)-Net over F₅ — Constructive and digital

Digital (15, 69, 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+54, 39)-Net over F₅ — Digital

Digital (15, 69, 39)-net over F₅, using

t-expansion [i] based on digital (14, 69, 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+54, 88)-Net in Base 5 — Upper bound on s

There is no (15, 69, 89)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁶⁹, 89, S₅, 54), but
- the linear programming bound shows that MÂ â‰¥ 161 188123 123059 113780 443374 341899 698265 478946 268558 502197 265625 / 80 086319 971801 > 5⁶⁹ [i]