MinT - Best Known (104−79, 104, s)-Nets in Base 5

Best Known (104−79, 104, s)-Nets in Base 5

(104−79, 104, 51)-Net over F₅ — Constructive and digital

Digital (25, 104, 51)-net over F₅, using

t-expansion [i] based on digital (22, 104, 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]

(104−79, 104, 55)-Net over F₅ — Digital

Digital (25, 104, 55)-net over F₅, using

t-expansion [i] based on digital (23, 104, 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]

(104−79, 104, 146)-Net in Base 5 — Upper bound on s

There is no (25, 104, 147)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁴, 147, S₅, 79), but
- the linear programming bound shows that MÂ â‰¥ 39372 091924 725703 857447 701903 838281 136301 223846 279850 589793 102440 375237 652259 166054 591332 795098 423957 824707 031250 / 7068 099469 950694 884565 750141 555625 095063 > 5¹⁰⁴ [i]