MinT - Best Known (24, 24+77, s)-Nets in Base 5

Best Known (24, 24+77, s)-Nets in Base 5

(24, 24+77, 51)-Net over F₅ — Constructive and digital

Digital (24, 101, 51)-net over F₅, using

t-expansion [i] based on digital (22, 101, 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]

(24, 24+77, 55)-Net over F₅ — Digital

Digital (24, 101, 55)-net over F₅, using

t-expansion [i] based on digital (23, 101, 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]

(24, 24+77, 138)-Net in Base 5 — Upper bound on s

There is no (24, 101, 139)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰¹, 139, S₅, 77), but
- the linear programming bound shows that MÂ â‰¥ 553223 981452 880155 821893 084339 174957 217162 975296 576958 360333 619289 274376 118470 399887 883104 383945 465087 890625 / 13 076155 305966 349341 916850 694551 657121 > 5¹⁰¹ [i]