Best Known (245−54, 245, s)-Nets in Base 3
(245−54, 245, 688)-Net over F3 — Constructive and digital
Digital (191, 245, 688)-net over F3, using
- 31 times duplication [i] based on digital (190, 244, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 61, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 61, 172)-net over F81, using
(245−54, 245, 1679)-Net over F3 — Digital
Digital (191, 245, 1679)-net over F3, using
(245−54, 245, 116603)-Net in Base 3 — Upper bound on s
There is no (191, 245, 116604)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 784 791969 805592 317820 584517 306871 275951 321036 671763 137605 311733 763123 921398 746718 819676 486676 361201 349227 031078 605137 > 3245 [i]