MinT - Best Known (23, 23+80, s)-Nets in Base 5

Best Known (23, 23+80, s)-Nets in Base 5

(23, 23+80, 51)-Net over F₅ — Constructive and digital

Digital (23, 103, 51)-net over F₅, using

t-expansion [i] based on digital (22, 103, 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, 23+80, 55)-Net over F₅ — Digital

Digital (23, 103, 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, 23+80, 122)-Net in Base 5 — Upper bound on s

There is no (23, 103, 123)-net in base 5, because

1 times m-reduction [i] would yield (23, 102, 123)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹⁰², 123, S₅, 79), but
  - the linear programming bound shows that MÂ â‰¥ 187995 484805 436527 043629 104100 322913 909820 870550 192173 364933 978518 820367 753505 706787 109375 / 805220 224324 162227 > 5¹⁰² [i]