Best Known (65, 65+94, s)-Nets in Base 3
(65, 65+94, 48)-Net over F3 — Constructive and digital
Digital (65, 159, 48)-net over F3, using
- t-expansion [i] based on digital (45, 159, 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+94, 64)-Net over F3 — Digital
Digital (65, 159, 64)-net over F3, using
- t-expansion [i] based on digital (49, 159, 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+94, 296)-Net in Base 3 — Upper bound on s
There is no (65, 159, 297)-net in base 3, because
- 1 times m-reduction [i] would yield (65, 158, 297)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3158, 297, S3, 93), but
- 3 times code embedding in larger space [i] would yield OA(3161, 300, S3, 93), but
- the linear programming bound shows that M ≥ 26 675190 910889 743112 227403 163412 369359 793844 655721 340317 557789 248012 220123 774642 492287 662763 607259 550327 271954 382919 241668 285384 889115 564887 322003 703190 344960 472589 597994 590619 753517 949291 094660 470697 925429 175559 939979 743324 110451 411335 715570 188254 780713 868528 411048 954236 118910 818343 352910 110829 710214 302673 465970 450572 495510 720207 187053 130206 312104 204688 171143 922695 455802 614479 243682 798668 670866 717591 124874 544160 256513 496999 336875 000087 224187 535562 861437 346904 969821 535412 890100 125065 793362 130779 728885 405778 821636 510376 269586 895972 042966 868865 941626 591333 496960 088019 966970 116228 152540 157724 275786 119268 421233 844937 211050 490123 736880 918613 436495 573375 165712 880240 231235 040282 427710 844230 770705 503023 135293 563133 809492 177994 719974 516594 483903 244782 008649 777615 845050 820063 330848 277964 044867 831391 753427 760033 026400 773599 077251 088957 350530 558786 061008 879219 719672 346972 082913 078932 769718 307279 997227 088300 034056 980064 795266 802190 679978 511197 534542 942047 142014 386236 664961 214736 623827 120270 295624 333822 864002 008337 729433 293926 596798 781992 567372 890301 092769 789734 508372 268894 921365 051538 201214 129104 777207 517709 750711 878103 426155 563565 876456 166605 245655 111232 927260 022531 559041 912470 093175 603382 449356 737556 756409 481782 128816 353292 459406 127856 785793 731706 144495 264763 419213 914725 787160 730792 922679 369321 / 317 854711 001440 227408 116447 323844 235016 863819 961132 906980 888738 898993 417370 129859 551299 749506 298788 458462 105856 187989 409602 224709 585917 603686 309727 040539 318106 981720 801637 618063 644440 217761 884512 214485 640966 463516 399277 058680 545590 791080 264501 584892 272443 311761 527991 663194 193138 004703 428647 982078 874359 628859 237769 797300 278331 605357 829263 747859 985532 495610 059515 775274 126044 445229 947472 808247 379473 754131 612059 845681 764715 065202 196864 581880 551107 512052 801706 019362 360167 808312 494982 320863 796028 041065 597292 217228 976968 376134 015697 477643 318365 235703 194976 052661 385575 674057 573514 338566 839540 156339 737752 516924 381266 352572 012223 998446 717765 099262 410350 744423 468642 745952 968914 568242 546191 608419 335140 815849 062960 046731 713199 054040 453821 369523 681565 689390 567998 110098 086354 110867 071145 054040 547884 262306 375132 328173 288468 949950 731142 341040 568015 272953 685838 194630 312333 482366 730447 168564 336591 759372 415662 857151 826694 840771 615395 891929 486472 995599 262608 611562 357785 595356 158865 852345 384258 842750 469505 493055 327949 213978 560719 159127 825952 070988 915082 774309 663948 982797 302349 781592 173448 833892 832789 450932 240153 038440 002744 677991 950143 554349 571799 017280 337410 933436 410471 376645 562857 065626 695183 742902 943702 473606 488254 774426 768330 > 3161 [i]
- 3 times code embedding in larger space [i] would yield OA(3161, 300, S3, 93), but
- extracting embedded orthogonal array [i] would yield OA(3158, 297, S3, 93), but