Best Known (45, 119, s)-Nets in Base 3
(45, 119, 48)-Net over F3 — Constructive and digital
Digital (45, 119, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
(45, 119, 56)-Net over F3 — Digital
Digital (45, 119, 56)-net over F3, using
- t-expansion [i] based on digital (40, 119, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(45, 119, 186)-Net over F3 — Upper bound on s (digital)
There is no digital (45, 119, 187)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3119, 187, F3, 74) (dual of [187, 68, 75]-code), but
- construction Y1 [i] would yield
- OA(3118, 149, S3, 74), but
- the linear programming bound shows that M ≥ 14631 013686 142997 953866 980562 476233 047154 143146 692997 967075 486096 911649 489501 / 62 737137 135696 970925 > 3118 [i]
- OA(368, 187, S3, 38), but
- the linear programming bound shows that M ≥ 4 185011 256460 307952 313976 653889 690485 861995 490330 218229 391251 955691 449885 824042 401792 / 14773 934323 743575 783185 881134 593137 934301 575737 911449 > 368 [i]
- OA(3118, 149, S3, 74), but
- construction Y1 [i] would yield
(45, 119, 216)-Net in Base 3 — Upper bound on s
There is no (45, 119, 217)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 654 638524 372023 414877 758292 895346 269335 981374 255100 133283 > 3119 [i]