Best Known (3, 3+66, s)-Nets in Base 25
(3, 3+66, 52)-Net over F25 — Constructive and digital
Digital (3, 69, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+66, 56)-Net over F25 — Digital
Digital (3, 69, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+66, 228)-Net in Base 25 — Upper bound on s
There is no (3, 69, 229)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2569, 229, S25, 66), but
- the linear programming bound shows that M ≥ 18 043494 936773 058917 524952 079538 007286 453827 830722 189805 010848 506401 936654 913731 317151 359689 887613 058090 209960 937500 / 6 226520 108029 254931 > 2569 [i]