MinT - Best Known (117−91, 117, s)-Nets in Base 5

Best Known (117−91, 117, s)-Nets in Base 5

(117−91, 117, 51)-Net over F₅ — Constructive and digital

Digital (26, 117, 51)-net over F₅, using

t-expansion [i] based on digital (22, 117, 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]

(117−91, 117, 55)-Net over F₅ — Digital

Digital (26, 117, 55)-net over F₅, using

t-expansion [i] based on digital (23, 117, 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]

(117−91, 117, 134)-Net in Base 5 — Upper bound on s

There is no (26, 117, 135)-net in base 5, because

1 times m-reduction [i] would yield (26, 116, 135)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹¹⁶, 135, S₅, 90), but
  - the linear programming bound shows that MÂ â‰¥ 1 876265 231422 762532 231153 304325 665211 759844 834664 773195 916087 633605 684459 325857 460498 809814 453125 / 1277 641347 875893 > 5¹¹⁶ [i]