Best Known (118−84, 118, s)-Nets in Base 16
(118−84, 118, 65)-Net over F16 — Constructive and digital
Digital (34, 118, 65)-net over F16, using
- t-expansion [i] based on digital (6, 118, 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
(118−84, 118, 104)-Net in Base 16 — Constructive
(34, 118, 104)-net in base 16, using
- 7 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
- base change [i] based on digital (9, 100, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 100, 104)-net over F32, using
(118−84, 118, 193)-Net over F16 — Digital
Digital (34, 118, 193)-net over F16, using
- t-expansion [i] based on digital (33, 118, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(118−84, 118, 2635)-Net in Base 16 — Upper bound on s
There is no (34, 118, 2636)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 12247 181806 697775 427972 260984 404339 761376 469380 300584 318445 289992 513862 221111 165223 926564 424220 508034 769464 363796 111196 881131 933912 621693 700906 > 16118 [i]