MinT - Best Known (20, 20+71, s)-Nets in Base 5

Best Known (20, 20+71, s)-Nets in Base 5

(20, 20+71, 43)-Net over F₅ — Constructive and digital

Digital (20, 91, 43)-net over F₅, using

t-expansion [i] based on digital (18, 91, 43)-net over F₅, using
- net from sequence [i] based on digital (18, 42)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 17, N(F)Â =Â 42, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(20, 20+71, 45)-Net over F₅ — Digital

Digital (20, 91, 45)-net over F₅, using

t-expansion [i] based on digital (19, 91, 45)-net over F₅, using
- net from sequence [i] based on digital (19, 44)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 19 and N(F) ≥ 45, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(20, 20+71, 108)-Net in Base 5 — Upper bound on s

There is no (20, 91, 109)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹¹, 109, S₅, 71), but
- the linear programming bound shows that MÂ â‰¥ 2276 405034 226668 958681 804882 276163 842780 292156 930954 661220 312118 530273 437500 / 412113 916071 > 5⁹¹ [i]