Best Known (61, 176, s)-Nets in Base 3
(61, 176, 48)-Net over F3 — Constructive and digital
Digital (61, 176, 48)-net over F3, using
- t-expansion [i] based on digital (45, 176, 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
(61, 176, 64)-Net over F3 — Digital
Digital (61, 176, 64)-net over F3, using
- t-expansion [i] based on digital (49, 176, 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
(61, 176, 218)-Net over F3 — Upper bound on s (digital)
There is no digital (61, 176, 219)-net over F3, because
- 1 times m-reduction [i] would yield digital (61, 175, 219)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3175, 219, F3, 114) (dual of [219, 44, 115]-code), but
- residual code [i] would yield OA(361, 104, S3, 38), but
- the linear programming bound shows that M ≥ 215738 553867 294765 547315 427144 658478 953384 447876 816406 609237 390217 341335 785320 530901 097095 689610 364315 585436 148743 / 1 653900 488288 762417 441699 879030 043019 631369 903205 462657 103479 100855 831115 771782 746875 > 361 [i]
- residual code [i] would yield OA(361, 104, S3, 38), but
- extracting embedded orthogonal array [i] would yield linear OA(3175, 219, F3, 114) (dual of [219, 44, 115]-code), but
(61, 176, 269)-Net in Base 3 — Upper bound on s
There is no (61, 176, 270)-net in base 3, because
- 1 times m-reduction [i] would yield (61, 175, 270)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 358898 103947 644432 548373 294490 567649 213348 676531 783733 401642 809217 677101 722149 735981 > 3175 [i]