Best Known (68, 164, s)-Nets in Base 3
(68, 164, 48)-Net over F3 — Constructive and digital
Digital (68, 164, 48)-net over F3, using
- t-expansion [i] based on digital (45, 164, 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
(68, 164, 72)-Net over F3 — Digital
Digital (68, 164, 72)-net over F3, using
- t-expansion [i] based on digital (67, 164, 72)-net over F3, using
- net from sequence [i] based on digital (67, 71)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 67 and N(F) ≥ 72, using
- net from sequence [i] based on digital (67, 71)-sequence over F3, using
(68, 164, 298)-Net in Base 3 — Upper bound on s
There is no (68, 164, 299)-net in base 3, because
- 1 times m-reduction [i] would yield (68, 163, 299)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3163, 299, S3, 95), but
- 1 times code embedding in larger space [i] would yield OA(3164, 300, S3, 95), but
- the linear programming bound shows that M ≥ 420 197808 209745 105934 997469 878774 335534 657438 481633 319457 949141 214544 181885 619274 260760 658504 606927 427368 316120 572622 878584 099507 264143 236850 984868 376799 975484 609009 128637 980723 613415 969226 260076 236295 272071 827245 928167 180285 376405 632155 035572 471070 030108 235540 892882 290990 097355 810341 953822 383811 081034 450692 264192 574448 446490 351336 253557 557704 445313 116994 214566 036978 130760 597156 952143 335021 231447 544219 589451 268175 528671 491965 312843 975318 540692 696738 648349 529885 764439 802807 683664 993571 127430 674089 471160 743508 689476 816517 707713 142612 559740 370207 792506 242525 658285 045490 017421 798410 961872 376274 471316 979056 309316 618899 743637 952012 603878 959343 957560 408715 945209 887818 931679 760275 564510 962401 578804 234708 066383 707446 512840 236435 009454 249865 690053 935897 787300 225600 904466 011308 647917 457436 159155 750933 518921 249434 095722 520640 023223 658412 634584 692906 013332 857931 923029 290151 772295 025432 626921 974608 799201 650348 249832 804381 973118 949946 665223 752917 756444 968574 674915 110787 464364 596421 063390 847264 693782 923601 933313 357498 622185 897711 366798 936343 128304 431823 149374 681537 743972 152136 394525 500032 270670 357715 758252 532320 273097 534447 273144 109238 209511 927545 919868 319998 874085 / 156 268121 813262 073288 165362 146966 891697 858218 013626 716915 224097 526322 273100 936219 218865 850463 760778 587195 127991 278635 449108 509855 385214 237578 815686 449357 075746 149677 373486 107528 877754 463576 146569 357261 196454 260435 399048 053425 756692 306537 911421 934363 328227 770814 638050 091705 686646 712134 771653 821273 142656 948452 347805 025825 830268 625728 370967 898619 391565 104611 802807 096870 734792 807769 541932 826098 210108 555055 813062 461280 248496 293097 239556 833929 756454 408382 788069 713113 255038 111209 236092 412126 821637 621839 450443 193568 843206 494427 785075 624911 984905 025475 420869 173576 525791 571508 631222 868446 975029 045183 760696 376059 216790 513573 094212 504625 893188 676847 044233 799794 781221 010967 759176 405596 372842 595197 661537 560411 641624 893931 796208 821534 483821 170865 539141 027608 544023 477353 720979 949006 689180 506380 708547 256440 422561 516955 090095 483263 063146 972694 372952 652004 403568 429371 840671 581276 353665 259069 721327 883009 168618 497976 742381 766500 025952 771455 993688 762464 054137 126936 381671 012400 760952 691258 444617 030777 926522 684910 307402 083422 216675 478132 261740 159333 517971 014559 726332 583724 072110 866146 490942 732032 > 3164 [i]
- 1 times code embedding in larger space [i] would yield OA(3164, 300, S3, 95), but
- extracting embedded orthogonal array [i] would yield OA(3163, 299, S3, 95), but