Best Known (1, 1+15, s)-Nets in Base 16
(1, 1+15, 24)-Net over F16 — Constructive and digital
Digital (1, 16, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
(1, 1+15, 25)-Net over F16 — Digital
Digital (1, 16, 25)-net over F16, using
- net from sequence [i] based on digital (1, 24)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
(1, 1+15, 73)-Net in Base 16 — Upper bound on s
There is no (1, 16, 74)-net in base 16, because
- 7 times m-reduction [i] would yield (1, 9, 74)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 69462 347566 > 169 [i]
- extracting embedded orthogonal array [i] would yield OA(169, 74, S16, 8), but
- the linear programming bound shows that M ≥ 108 985717 478079 332352 / 1552 440097 > 169 [i]