Best Known (56, 128, s)-Nets in Base 3
(56, 128, 48)-Net over F3 — Constructive and digital
Digital (56, 128, 48)-net over F3, using
- t-expansion [i] based on digital (45, 128, 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
(56, 128, 64)-Net over F3 — Digital
Digital (56, 128, 64)-net over F3, using
- t-expansion [i] based on digital (49, 128, 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
(56, 128, 299)-Net in Base 3 — Upper bound on s
There is no (56, 128, 300)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3128, 300, S3, 72), but
- the linear programming bound shows that M ≥ 20105 026358 378154 656765 820483 826998 529185 161677 233438 691803 764372 266848 127446 552020 818459 373227 566178 361692 915780 481064 777374 154031 815531 398279 750479 764084 102770 380036 285777 645725 943494 548634 893168 062433 760041 051092 584910 391073 288061 457106 061386 971743 448871 475162 952657 626998 146414 107626 446169 791194 634834 797716 193399 660858 581124 206930 206547 562897 630997 384121 972936 842497 695054 397124 776767 582032 124167 907940 365877 846591 019500 058777 164209 725207 431911 582419 159869 379642 558209 808464 940930 388063 328560 171466 037434 061891 975526 066524 632890 904700 683302 256508 588500 231686 550829 379057 740690 521956 697800 854894 802471 061613 037500 262606 493729 235742 764240 583638 230026 796194 285004 598967 052090 155974 474968 245475 728373 748835 290437 546875 641616 549381 305055 214782 544454 793083 562934 578193 894989 402098 101545 263731 653416 295641 515603 506818 392147 208951 562240 / 1000 545331 118087 428407 378789 317622 389644 163050 775594 978831 531690 280336 634233 579194 555561 764681 376803 637545 272384 040706 719064 585805 249935 209613 469592 204231 451865 040292 174498 471324 032487 591568 983024 547979 853089 241314 855243 494074 275726 386881 057639 272248 082290 451423 714075 023062 328096 129694 173880 428533 903689 081427 182358 693618 149743 898962 248617 437911 837851 348716 854256 546953 777143 833694 930961 146713 943079 260784 490544 488584 829691 187610 588566 442382 367303 467421 555969 580585 987292 645278 204991 051770 453459 261698 382876 086414 850633 021438 921105 681484 609843 612361 828928 989493 583333 906751 944089 861126 895489 839380 340851 518761 970626 402236 004092 773764 601044 086113 497615 654392 112296 484285 603913 579065 834166 381751 297436 128369 324545 928232 326394 739309 701680 693869 167145 199548 260039 841420 776827 > 3128 [i]