Best Known (58, 58+86, s)-Nets in Base 3
(58, 58+86, 48)-Net over F3 — Constructive and digital
Digital (58, 144, 48)-net over F3, using
- t-expansion [i] based on digital (45, 144, 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
(58, 58+86, 64)-Net over F3 — Digital
Digital (58, 144, 64)-net over F3, using
- t-expansion [i] based on digital (49, 144, 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
(58, 58+86, 293)-Net in Base 3 — Upper bound on s
There is no (58, 144, 294)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 508 322443 349604 418186 396506 995311 283541 690885 152425 317613 488458 252625 > 3144 [i]
- extracting embedded orthogonal array [i] would yield OA(3144, 294, S3, 86), but
- 6 times code embedding in larger space [i] would yield OA(3150, 300, S3, 86), but
- the linear programming bound shows that M ≥ 320472 570574 691719 523986 851184 828244 068642 952523 532086 227969 214463 840225 094811 826977 656102 844369 865339 986639 083879 693894 808305 461026 319944 045512 935142 298704 110828 049518 550374 084559 786715 490131 370172 966650 703473 854471 827384 793724 020502 777717 770080 736224 783319 827244 328466 997320 450901 584543 279387 965296 713104 287899 641956 409776 507609 809996 605462 983848 857613 450566 509143 241012 807511 597635 169156 883770 208851 325079 226339 816569 522938 562352 390371 208080 804722 014493 134320 254274 697380 980877 442786 522548 218255 365131 265551 070640 159606 206725 853033 718784 954345 786753 372524 465889 456945 180949 989577 628711 007289 066562 482444 851833 225823 422334 872927 642143 442178 393759 061901 755225 448692 226592 902085 550462 060295 191131 004141 776053 518305 052597 843515 872550 959892 864323 383119 175098 537529 297854 942453 709193 985264 959767 166978 799649 254703 858372 362876 551961 769028 543725 388246 789414 319774 747524 157312 032257 681308 291327 108697 109997 459312 884181 683679 304057 474957 793637 544573 500299 828805 385006 850306 506073 050392 425508 107933 562101 812517 641748 572897 082673 153793 437585 754734 482030 057201 816648 604475 862271 110297 790112 464029 932254 205761 401986 086459 899095 332005 541226 709622 164177 767292 672316 364538 112075 601261 365704 273185 517759 160348 672965 933868 780465 145498 126183 747422 252859 994656 834629 766761 579443 380610 410938 659744 545023 259037 081614 550578 930599 824346 941822 820846 085351 547121 226673 628758 846352 613871 813690 477916 426066 025801 086892 339708 334876 886601 823420 879592 932274 663085 445747 160361 493374 700747 486684 411558 809854 787980 210889 508088 350633 212390 747479 386745 / 638832 777598 265518 200417 470998 797460 617573 738700 334620 240141 370517 668148 454825 916406 950735 342709 290709 529760 004487 785210 100547 919315 069215 857506 056855 030402 045160 735491 996216 662746 264459 918360 269263 717896 365435 137786 674573 285682 824769 638705 858182 310249 809961 813300 707077 360934 865303 848240 820257 968646 994312 615928 000570 650286 553805 902759 514705 437223 014407 922908 872632 634457 318183 882163 123558 603295 646503 783086 247660 720214 468897 428200 625614 157667 456442 201553 205089 910423 339198 290362 757004 780379 048647 838254 263141 786184 762133 266433 656373 540425 193131 201348 659973 011858 584390 309662 968609 515014 860128 652152 055057 663817 508832 262471 951064 471189 371460 220843 896236 257708 691802 250763 157615 007144 029540 631610 125461 917345 744579 474138 674756 816285 143955 820478 394922 353292 205816 847920 118129 629207 772706 809884 367165 519129 359329 158169 842239 923612 892240 402032 925487 544367 980953 163977 677199 353422 433495 783417 358992 911869 906031 895615 230548 984142 651679 200071 211873 725673 410529 200237 466565 721659 175011 433775 101363 555053 373547 592452 889392 143364 235261 200042 932228 463799 872307 411334 899092 597048 081542 430468 510728 730637 917181 110140 476499 366477 228758 053406 225978 397297 541914 502972 878766 556833 170164 485911 397559 881242 901502 485019 320299 459650 768600 076637 468723 904909 839412 170021 509410 183402 945247 152400 912800 443706 015008 922381 396255 351843 038371 563208 017197 990894 818513 323711 316532 771782 997562 806217 746164 055813 793330 481735 693161 278550 889195 912683 424975 261291 026383 737669 137644 > 3150 [i]
- 6 times code embedding in larger space [i] would yield OA(3150, 300, S3, 86), but