Best Known (65, 65+91, s)-Nets in Base 3
(65, 65+91, 48)-Net over F3 — Constructive and digital
Digital (65, 156, 48)-net over F3, using
- t-expansion [i] based on digital (45, 156, 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
(65, 65+91, 64)-Net over F3 — Digital
Digital (65, 156, 64)-net over F3, using
- t-expansion [i] based on digital (49, 156, 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
(65, 65+91, 297)-Net in Base 3 — Upper bound on s
There is no (65, 156, 298)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3156, 298, S3, 91), but
- 2 times code embedding in larger space [i] would yield OA(3158, 300, S3, 91), but
- the linear programming bound shows that M ≥ 3 051120 446125 392318 693650 115982 701326 276402 991766 382987 515884 816769 864443 105877 946553 249597 524348 297732 940020 387717 173766 521402 354337 456968 218171 351500 759541 451365 069755 815152 220825 341005 104291 166298 503949 069130 278681 536642 232767 718071 066817 948748 987163 040136 044741 351868 903974 550514 181559 372934 092286 622006 042417 542551 434409 081210 362746 472254 456465 728273 544541 568714 491514 372285 519269 434620 678896 833680 124791 196668 035162 469508 363042 756808 716047 614517 620936 228806 459299 538849 136258 245619 657382 513747 047381 649868 669950 476233 929591 934910 182438 464702 770175 700143 150796 485499 532502 855388 239545 522624 495367 158954 050024 693894 205441 748060 746121 309209 430260 307813 887843 781012 363796 376141 281161 390589 196091 361438 325804 015313 300246 828951 659652 061261 289201 744491 130049 952194 390952 070977 073850 222004 182482 046831 209954 487240 852009 012400 321661 314785 706436 644681 752892 629254 854381 483596 055039 441761 116360 912144 688230 465444 473642 226212 776960 460655 121348 284267 398920 350423 543887 057109 404500 662819 780678 451296 618467 664057 344485 314695 816492 494292 927957 121964 205375 161234 605488 346608 908140 759531 633631 044868 278318 153116 350090 119462 602899 821652 460603 197656 549229 726215 674271 579321 266152 166188 634994 793072 471335 044366 657508 228468 560082 165635 174187 394687 924549 743047 966663 698671 472456 851395 534185 521227 867371 679471 387576 776862 194451 565635 390569 516273 427280 076592 789367 685972 921640 552187 550075 280435 214546 341613 / 1089 771287 466942 716237 668944 604873 074829 339690 941071 533525 403027 900901 152793 953784 799255 804184 231135 486051 774554 142862 242860 526841 860449 912701 417150 298890 919050 657959 681378 121919 412674 834978 160254 792450 254023 662703 881966 457551 711576 220623 119073 516470 079435 753679 367264 053083 901173 185034 989567 882415 854622 955008 982857 775248 464098 446007 260931 562332 714727 196502 728457 545452 096394 374780 251710 102591 364210 168604 901579 438222 118962 215240 715318 915316 352131 867720 323310 079258 007961 675345 529457 448932 582465 257437 261039 702371 272935 107251 935672 977045 310263 507117 876208 409941 470538 294779 130635 027425 462527 178499 141497 733835 274860 530204 985139 649311 844646 887936 857160 599908 663811 404019 635133 551601 084789 659403 255054 396250 577552 933017 507564 802125 601338 178382 159293 152770 800665 035592 681892 462554 265886 874966 988367 990569 852892 117864 266400 479788 220061 151976 358920 874138 756943 210906 525003 812636 632965 175363 498771 955845 100184 641746 017032 604288 025904 736193 497607 587090 516128 054995 749705 628332 452364 898747 215537 906825 251425 835838 050289 536787 051480 277131 212903 760894 160694 402240 094442 355552 069246 935930 601636 910808 342323 454636 542580 058663 266972 691310 216077 169727 539435 048320 197002 639743 668381 252018 866527 861533 867668 406301 239891 941580 560250 422093 846396 338895 874848 078544 300857 018969 863443 659160 827611 835460 955990 790074 884280 305313 144085 > 3158 [i]
- 2 times code embedding in larger space [i] would yield OA(3158, 300, S3, 91), but