MinT - Best Known (112−86, 112, s)-Nets in Base 5

Best Known (112−86, 112, s)-Nets in Base 5

(112−86, 112, 51)-Net over F₅ — Constructive and digital

Digital (26, 112, 51)-net over F₅, using

t-expansion [i] based on digital (22, 112, 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]

(112−86, 112, 55)-Net over F₅ — Digital

Digital (26, 112, 55)-net over F₅, using

t-expansion [i] based on digital (23, 112, 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]

(112−86, 112, 138)-Net in Base 5 — Upper bound on s

There is no (26, 112, 139)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹², 139, S₅, 86), but
- the linear programming bound shows that MÂ â‰¥ 2 082589 264522 932824 279618 514424 429978 311367 037622 562595 373942 873067 107939 277775 585651 397705 078125 / 1 034045 105594 725224 > 5¹¹² [i]