Best Known (60, 163, s)-Nets in Base 3
(60, 163, 48)-Net over F3 — Constructive and digital
Digital (60, 163, 48)-net over F3, using
- t-expansion [i] based on digital (45, 163, 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
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(60, 163, 64)-Net over F3 — Digital
Digital (60, 163, 64)-net over F3, using
- t-expansion [i] based on digital (49, 163, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(60, 163, 264)-Net over F3 — Upper bound on s (digital)
There is no digital (60, 163, 265)-net over F3, because
- 1 times m-reduction [i] would yield digital (60, 162, 265)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3162, 265, F3, 102) (dual of [265, 103, 103]-code), but
- residual code [i] would yield OA(360, 162, S3, 34), but
- the linear programming bound shows that M ≥ 68980 367968 436452 870293 317186 511729 045056 682286 749727 903703 040000 000000 / 1 592376 446885 204670 935611 188490 612206 288097 > 360 [i]
- residual code [i] would yield OA(360, 162, S3, 34), but
- extracting embedded orthogonal array [i] would yield linear OA(3162, 265, F3, 102) (dual of [265, 103, 103]-code), but
(60, 163, 277)-Net in Base 3 — Upper bound on s
There is no (60, 163, 278)-net in base 3, because
- 1 times m-reduction [i] would yield (60, 162, 278)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 199990 777482 418360 372802 079588 524257 542719 672539 594850 333437 163804 225937 791937 > 3162 [i]