Best Known (244, 244+∞, s)-Nets in Base 3
(244, 244+∞, 117)-Net over F3 — Constructive and digital
Digital (244, m, 117)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (244, 116)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 116)-sequence over F9, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- base reduction for sequences [i] based on digital (64, 116)-sequence over F9, using
(244, 244+∞, 163)-Net over F3 — Digital
Digital (244, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (244, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(244, 244+∞, 503)-Net in Base 3 — Upper bound on s
There is no (244, m, 504)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (244, 3016, 504)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(33016, 504, S3, 6, 2772), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 427 036623 904025 803070 740228 916586 680196 559431 451600 240304 452383 019016 403099 498752 482904 651276 800829 774201 165749 550380 094066 168316 684517 479695 058040 268866 446574 429993 135944 108588 575848 813436 444187 869677 603720 926643 074987 225144 084461 276956 232405 313646 333796 455774 916584 808597 902897 180987 150430 518218 385681 645609 178339 017510 948157 205303 110350 145658 876230 375834 553359 206148 638139 898398 500651 844374 883606 697009 213702 463190 875752 323396 305823 621923 238373 603042 228560 360487 849234 606542 128433 574748 787396 756671 239821 548194 438912 552238 697820 817966 031859 329405 431135 700396 607559 789603 370566 459907 557971 286666 189929 767257 700361 815264 507751 802068 339681 520580 397489 139290 991396 965334 232114 059417 262657 046176 374579 781081 566767 691720 030407 309592 015751 991195 351388 374706 460756 675122 580045 367853 535102 716402 778245 744018 037223 330523 211229 029773 896502 431733 497334 332391 950092 618312 543471 437215 733984 810440 198116 805848 044727 275423 101856 383366 811168 810237 707206 926942 545960 205233 815851 995821 577006 277787 875475 249062 790219 559804 648332 836702 145734 658627 171068 909035 532247 958759 515809 604629 266248 116656 510496 436265 953097 401853 580178 845911 332342 038555 709618 743718 987821 262083 171147 750834 214160 956109 569001 984909 718105 908792 907673 431068 319315 221175 447946 593260 938450 129376 047785 890687 667419 880362 512342 550559 584841 992656 906842 191837 505007 205439 515110 639609 584736 221426 140442 864391 521383 401898 458161 735608 291699 462359 704866 103336 107562 053438 468377 931599 713219 050691 553253 / 2773 > 33016 [i]
- extracting embedded OOA [i] would yield OOA(33016, 504, S3, 6, 2772), but