Best Known (123−108, 123, s)-Nets in Base 5
(123−108, 123, 36)-Net over F5 — Constructive and digital
Digital (15, 123, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(123−108, 123, 39)-Net over F5 — Digital
Digital (15, 123, 39)-net over F5, using
- t-expansion [i] based on digital (14, 123, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(123−108, 123, 83)-Net in Base 5 — Upper bound on s
There is no (15, 123, 84)-net in base 5, because
- 51 times m-reduction [i] would yield (15, 72, 84)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(572, 84, S5, 57), but
- the linear programming bound shows that M ≥ 1 900530 175401 836385 784548 610899 946652 352809 906005 859375 / 8671 > 572 [i]
- extracting embedded orthogonal array [i] would yield OA(572, 84, S5, 57), but