Best Known (66−38, 66, s)-Nets in Base 16
(66−38, 66, 103)-Net over F16 — Constructive and digital
Digital (28, 66, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (6, 44, 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
- digital (3, 22, 38)-net over F16, using
(66−38, 66, 128)-Net in Base 16 — Constructive
(28, 66, 128)-net in base 16, using
- 3 times m-reduction [i] based on (28, 69, 128)-net in base 16, using
- base change [i] based on digital (5, 46, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- base change [i] based on digital (5, 46, 128)-net over F64, using
(66−38, 66, 156)-Net over F16 — Digital
Digital (28, 66, 156)-net over F16, using
- t-expansion [i] based on digital (27, 66, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
(66−38, 66, 161)-Net in Base 16
(28, 66, 161)-net in base 16, using
- base change [i] based on digital (6, 44, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
(66−38, 66, 8040)-Net in Base 16 — Upper bound on s
There is no (28, 66, 8041)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 29 652127 390210 705030 355246 524441 631202 391728 201620 648117 345250 795869 007998 651536 > 1666 [i]