Best Known (78, 123, s)-Nets in Base 16
(78, 123, 583)-Net over F16 — Constructive and digital
Digital (78, 123, 583)-net over F16, using
- 161 times duplication [i] based on digital (77, 122, 583)-net over F16, using
- (u, u+v)-construction [i] based on
- 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 (49, 94, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 47, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 47, 259)-net over F256, using
- digital (6, 28, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(78, 123, 2694)-Net over F16 — Digital
Digital (78, 123, 2694)-net over F16, using
(78, 123, 2871789)-Net in Base 16 — Upper bound on s
There is no (78, 123, 2871790)-net in base 16, because
- 1 times m-reduction [i] would yield (78, 122, 2871790)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 799 171256 818505 455665 646771 088520 696428 578332 168236 588479 433480 244512 531277 243681 971680 768847 805211 669001 740664 448905 355852 529606 428756 266496 169576 > 16122 [i]