Best Known (59−42, 59, s)-Nets in Base 5
(59−42, 59, 42)-Net over F5 — Constructive and digital
Digital (17, 59, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(59−42, 59, 179)-Net in Base 5 — Upper bound on s
There is no (17, 59, 180)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(559, 180, S5, 42), but
- the linear programming bound shows that M ≥ 3 021148 639276 435712 120868 907956 910470 245775 845789 640240 114564 088255 161294 682693 551294 505596 160888 671875 / 17 038157 362598 071466 840534 455766 137987 897648 392665 955197 142131 > 559 [i]