Best Known (18, 18+62, s)-Nets in Base 5
(18, 18+62, 43)-Net over F5 — Constructive and digital
Digital (18, 80, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(18, 18+62, 104)-Net in Base 5 — Upper bound on s
There is no (18, 80, 105)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(580, 105, S5, 62), but
- the linear programming bound shows that M ≥ 1251 664478 049512 095288 777876 054739 889022 382470 784577 890299 260616 302490 234375 / 13 833453 004647 161886 > 580 [i]