Best Known (61, 162, s)-Nets in Base 3
(61, 162, 48)-Net over F3 — Constructive and digital
Digital (61, 162, 48)-net over F3, using
- t-expansion [i] based on digital (45, 162, 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, 162, 64)-Net over F3 — Digital
Digital (61, 162, 64)-net over F3, using
- t-expansion [i] based on digital (49, 162, 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, 162, 288)-Net in Base 3 — Upper bound on s
There is no (61, 162, 289)-net in base 3, because
- 1 times m-reduction [i] would yield (61, 161, 289)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 73244 567361 728789 925849 530958 986050 774109 505640 013689 624764 446393 291160 367881 > 3161 [i]
- extracting embedded orthogonal array [i] would yield OA(3161, 289, S3, 100), but
- 11 times code embedding in larger space [i] would yield OA(3172, 300, S3, 100), but
- the linear programming bound shows that M ≥ 789 403276 438135 140451 372825 824228 379367 899944 057443 291498 014921 925237 917748 937414 241695 245728 331144 464103 216267 979541 356266 316683 022919 355426 962563 330854 371838 671571 387128 425893 447707 746596 269217 040262 981195 818548 813536 413411 532054 321158 325616 876310 810983 146955 865980 609079 539008 391037 513332 085310 083581 512187 633436 787153 922061 074266 954725 488408 543430 310412 313802 563555 027287 546534 816308 929019 430112 623316 372783 834397 972278 972158 681323 724618 383243 208070 471392 592337 873475 425583 406319 352712 977754 915924 512023 772235 552467 138174 957800 021598 148710 118083 212210 532653 307776 999157 385997 398383 398805 508783 825887 248174 715555 547610 315697 465599 916080 650185 003290 809733 497145 706436 410080 954096 168313 592565 622410 771908 368264 082347 051470 278868 292149 220146 785915 592925 413520 275611 257426 001567 236704 888467 960238 140184 458567 / 53882 169159 487398 346703 604024 817441 746848 962337 701283 311075 750031 836665 381648 513188 060657 334377 281347 144343 150786 129187 710530 062902 097699 848578 669505 932556 799525 097842 496584 133844 577313 681821 603371 239203 169613 531315 741108 340890 861606 165222 610392 053826 563898 089048 222034 310516 544636 065160 953419 864465 322591 509155 952401 041651 773138 967213 171573 990718 546129 811295 644445 438621 001913 480906 909347 150970 432582 852352 737029 868277 110166 403098 523633 658117 156665 108053 318320 025656 323618 337383 698591 996112 441563 952085 922899 603301 774723 703246 549620 458641 304537 095771 309961 893937 043136 442928 636615 439975 550019 139611 600291 115359 456227 599391 017758 895732 588122 778596 389054 342179 669784 277462 527291 886280 264698 449918 122493 018549 817345 041402 167296 > 3172 [i]
- 11 times code embedding in larger space [i] would yield OA(3172, 300, S3, 100), but