MinT - Best Known (4, 82, s)-Nets in Base 25

Best Known (4, 82, s)-Nets in Base 25

(4, 82, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 82, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(4, 82, 267)-Net in Base 25 — Upper bound on s

There is no (4, 82, 268)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸², 268, S₂₅, 78), but
- the linear programming bound shows that MÂ â‰¥ 514794 201288 959391 330565 142142 961407 437137 948223 723651 956019 454500 785550 598058 711548 114831 964345 043809 842122 906061 945286 637637 764215 469360 351562 500000 / 119283 405761 786899 533134 222153 422853 > 25⁸² [i]