Best Known (16, 51, s)-Nets in Base 16
(16, 51, 65)-Net over F16 — Constructive and digital
Digital (16, 51, 65)-net over F16, using
- t-expansion [i] based on digital (6, 51, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(16, 51, 76)-Net in Base 16 — Constructive
(16, 51, 76)-net in base 16, using
- 4 times m-reduction [i] based on (16, 55, 76)-net in base 16, using
- base change [i] based on digital (5, 44, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 44, 76)-net over F32, using
(16, 51, 98)-Net over F16 — Digital
Digital (16, 51, 98)-net over F16, using
- t-expansion [i] based on digital (15, 51, 98)-net over F16, using
- net from sequence [i] based on digital (15, 97)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 15 and N(F) ≥ 98, using
- net from sequence [i] based on digital (15, 97)-sequence over F16, using
(16, 51, 1655)-Net in Base 16 — Upper bound on s
There is no (16, 51, 1656)-net in base 16, because
- 1 times m-reduction [i] would yield (16, 50, 1656)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 610862 684853 167624 160458 826124 463543 502864 750744 045779 813631 > 1650 [i]