MinT - Best Known (24, 24+79, s)-Nets in Base 5

Best Known (24, 24+79, s)-Nets in Base 5

(24, 24+79, 51)-Net over F₅ — Constructive and digital

Digital (24, 103, 51)-net over F₅, using

t-expansion [i] based on digital (22, 103, 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+79, 55)-Net over F₅ — Digital

Digital (24, 103, 55)-net over F₅, using

t-expansion [i] based on digital (23, 103, 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+79, 131)-Net in Base 5 — Upper bound on s

There is no (24, 103, 132)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰³, 132, S₅, 79), but
- the linear programming bound shows that MÂ â‰¥ 18 668623 082441 491414 219932 623374 983300 355590 950940 056827 779545 134404 770578 839816 153049 468994 140625 / 18 483143 804372 869280 393301 > 5¹⁰³ [i]