MinT - Best Known (104−80, 104, s)-Nets in Base 5

Best Known (104−80, 104, s)-Nets in Base 5

(104−80, 104, 51)-Net over F₅ — Constructive and digital

Digital (24, 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]

(104−80, 104, 55)-Net over F₅ — Digital

Digital (24, 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]

(104−80, 104, 129)-Net in Base 5 — Upper bound on s

There is no (24, 104, 130)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁴, 130, S₅, 80), but
- the linear programming bound shows that MÂ â‰¥ 372248 511648 309238 734040 027156 381714 489783 833276 916155 848035 305808 707562 391646 206378 936767 578125 / 73973 184294 142994 301441 > 5¹⁰⁴ [i]