Best Known (57, 57+79, s)-Nets in Base 3
(57, 57+79, 48)-Net over F3 — Constructive and digital
Digital (57, 136, 48)-net over F3, using
- t-expansion [i] based on digital (45, 136, 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
(57, 57+79, 64)-Net over F3 — Digital
Digital (57, 136, 64)-net over F3, using
- t-expansion [i] based on digital (49, 136, 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
(57, 57+79, 296)-Net in Base 3 — Upper bound on s
There is no (57, 136, 297)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3136, 297, S3, 79), but
- 3 times code embedding in larger space [i] would yield OA(3139, 300, S3, 79), but
- the linear programming bound shows that M ≥ 19 181248 501504 127154 288212 288625 035241 144258 010498 755617 509552 073481 387350 102439 967710 345904 398761 193055 420385 948681 881273 528492 881589 850809 670273 824345 667715 609388 993345 015617 564755 414881 039518 996589 722385 147608 382097 624568 403070 568838 094838 394819 409379 689156 862926 725079 583710 319888 380339 778609 130702 915458 302332 581793 724418 440047 224504 576758 746393 453832 866649 999631 620686 325702 924884 898320 968112 660437 439721 974299 585583 871303 992146 245955 998954 014797 185654 727682 287586 238275 765970 332150 595903 890580 377617 853493 212989 778771 595996 138719 904953 492782 606967 897328 449502 229205 193738 732846 217323 088245 105623 625637 429524 261765 641946 266773 623216 509594 895910 403107 979406 600640 888304 672088 866481 739213 776118 162550 749111 417881 411959 390365 249623 665708 032893 866576 522283 105589 858294 610125 754276 337982 775377 967963 796249 974946 551498 797464 246840 353567 485557 404835 585975 802427 269026 003358 127599 446552 691424 610232 426209 939890 919971 325772 830974 020082 799672 235691 435765 251565 138744 633886 889246 016376 275768 845505 339310 062131 639821 564148 375067 394307 796377 183132 529029 165012 527268 357266 116968 625990 498748 570323 811337 693880 717219 346270 168774 815438 900141 950931 113116 238955 751181 148304 818809 671563 986485 980547 411781 867770 404963 089216 767223 085969 618083 440721 247455 / 6 060857 468802 721042 584512 863723 173636 536031 401637 525420 600093 082187 142150 212735 548769 848243 908102 023798 756657 465334 138720 212395 312977 735933 570386 195923 217509 744346 233954 942445 559347 319546 628280 167414 907222 628234 149823 338127 606414 453869 788187 514805 527326 335061 730320 469485 186890 182274 600364 208884 194054 081028 288147 884291 935906 617196 358172 327198 089157 828858 814938 493548 825810 756043 177194 203601 186583 755643 547669 600735 139599 061510 557140 827993 690636 999981 546338 495017 948609 916788 693774 356282 474602 201338 790745 142787 830802 997931 940492 997466 088076 726686 365681 412089 318447 636091 446144 979654 140445 434543 136492 266149 318669 562678 370046 399297 269500 588687 593665 002386 427203 686381 732054 043000 639188 536502 683529 742315 436029 380811 213459 043180 502717 406062 727832 209443 539767 886217 791231 914013 648684 497794 505509 765848 526955 001330 581178 534761 362095 697442 628465 070636 779218 950050 316868 407903 841629 602519 901796 008386 501224 891630 169463 840254 137474 492568 632097 204366 223813 185150 092855 180301 171393 550105 504423 133189 225172 773005 675042 295333 089739 411049 437189 196804 471804 497528 891795 732169 377674 153606 262366 648481 373746 308343 809323 379691 613916 830480 693562 608807 944213 816050 699713 883590 657272 008756 > 3139 [i]
- 3 times code embedding in larger space [i] would yield OA(3139, 300, S3, 79), but