MinT - Best Known (25, 109, s)-Nets in Base 5

Best Known (25, 109, s)-Nets in Base 5

(25, 109, 51)-Net over F₅ — Constructive and digital

Digital (25, 109, 51)-net over F₅, using

t-expansion [i] based on digital (22, 109, 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]

(25, 109, 55)-Net over F₅ — Digital

Digital (25, 109, 55)-net over F₅, using

t-expansion [i] based on digital (23, 109, 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]

(25, 109, 132)-Net in Base 5 — Upper bound on s

There is no (25, 109, 133)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁹, 133, S₅, 84), but
- the linear programming bound shows that MÂ â‰¥ 152 145125 324345 787757 789441 319422 558782 400879 491367 664164 865047 826680 211073 835380 375385 284423 828125 / 8830 552083 085959 394077 > 5¹⁰⁹ [i]