MinT - Best Known (23, 101, s)-Nets in Base 5

Best Known (23, 101, s)-Nets in Base 5

(23, 101, 51)-Net over F₅ — Constructive and digital

Digital (23, 101, 51)-net over F₅, using

t-expansion [i] based on digital (22, 101, 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]

(23, 101, 55)-Net over F₅ — Digital

Digital (23, 101, 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]

(23, 101, 124)-Net in Base 5 — Upper bound on s

There is no (23, 101, 125)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰¹, 125, S₅, 78), but
- the linear programming bound shows that MÂ â‰¥ 191597 231611 815617 608519 333314 720860 653095 776634 548264 016899 565831 408835 947513 580322 265625 / 3 761500 410791 004713 > 5¹⁰¹ [i]