MinT - Best Known (113−88, 113, s)-Nets in Base 5

Best Known (113−88, 113, s)-Nets in Base 5

(113−88, 113, 51)-Net over F₅ — Constructive and digital

Digital (25, 113, 51)-net over F₅, using

t-expansion [i] based on digital (22, 113, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(113−88, 113, 55)-Net over F₅ — Digital

Digital (25, 113, 55)-net over F₅, using

t-expansion [i] based on digital (23, 113, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(113−88, 113, 130)-Net in Base 5 — Upper bound on s

There is no (25, 113, 131)-net in base 5, because

1 times m-reduction [i] would yield (25, 112, 131)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹¹², 131, S₅, 87), but
  - the linear programming bound shows that MÂ â‰¥ 64819 052034 878709 570998 680623 667131 742908 124355 154035 091397 535239 821081 631816 923618 316650 390625 / 25832 927656 150384 > 5¹¹² [i]