Best Known (19, 19+22, s)-Nets in Base 16
(19, 19+22, 98)-Net over F16 — Constructive and digital
Digital (19, 41, 98)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (6, 28, 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 (2, 13, 33)-net over F16, using
(19, 19+22, 134)-Net over F16 — Digital
Digital (19, 41, 134)-net over F16, using
(19, 19+22, 150)-Net in Base 16 — Constructive
(19, 41, 150)-net in base 16, using
- 1 times m-reduction [i] based on (19, 42, 150)-net in base 16, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
(19, 19+22, 10063)-Net in Base 16 — Upper bound on s
There is no (19, 41, 10064)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 23 390816 327546 793565 496425 002279 720129 375837 681811 > 1641 [i]