MinT - Best Known (23, 98, s)-Nets in Base 5

Best Known (23, 98, s)-Nets in Base 5

(23, 98, 51)-Net over F₅ — Constructive and digital

Digital (23, 98, 51)-net over F₅, using

t-expansion [i] based on digital (22, 98, 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, 98, 55)-Net over F₅ — Digital

Digital (23, 98, 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, 98, 131)-Net in Base 5 — Upper bound on s

There is no (23, 98, 132)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁸, 132, S₅, 75), but
- the linear programming bound shows that MÂ â‰¥ 196863 250288 266468 664413 735778 743663 339890 740365 086691 722354 243772 041826 332497 294060 885906 219482 421875 / 604 066622 879900 192636 995281 364531 > 5⁹⁸ [i]