MinT - Best Known (25, 25+80, s)-Nets in Base 5

Best Known (25, 25+80, s)-Nets in Base 5

(25, 25+80, 51)-Net over F₅ — Constructive and digital

Digital (25, 105, 51)-net over F₅, using

t-expansion [i] based on digital (22, 105, 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]

(25, 25+80, 55)-Net over F₅ — Digital

Digital (25, 105, 55)-net over F₅, using

t-expansion [i] based on digital (23, 105, 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]

(25, 25+80, 142)-Net in Base 5 — Upper bound on s

There is no (25, 105, 143)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁵, 143, S₅, 80), but
- the linear programming bound shows that MÂ â‰¥ 301216 072330 089828 190635 775379 201826 771027 089956 612676 918091 885231 465476 037426 842736 977050 662972 033023 834228 515625 / 11043 457750 145595 736844 873257 449421 340073 > 5¹⁰⁵ [i]