MinT - Best Known (125−97, 125, s)-Nets in Base 5

Best Known (125−97, 125, s)-Nets in Base 5

(125−97, 125, 51)-Net over F₅ — Constructive and digital

Digital (28, 125, 51)-net over F₅, using

t-expansion [i] based on digital (22, 125, 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]

(125−97, 125, 55)-Net over F₅ — Digital

Digital (28, 125, 55)-net over F₅, using

t-expansion [i] based on digital (23, 125, 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]

(125−97, 125, 143)-Net in Base 5 — Upper bound on s

There is no (28, 125, 144)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²⁵, 144, S₅, 97), but
- the linear programming bound shows that MÂ â‰¥ 18 218394 513527 273846 281585 774804 909562 492345 008682 453154 545363 184502 182463 120334 432460 367679 595947 265625 / 5328 965246 756697 > 5¹²⁵ [i]