Best Known (68, 68+98, s)-Nets in Base 3
(68, 68+98, 48)-Net over F3 — Constructive and digital
Digital (68, 166, 48)-net over F3, using
- t-expansion [i] based on digital (45, 166, 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, 68+98, 72)-Net over F3 — Digital
Digital (68, 166, 72)-net over F3, using
- t-expansion [i] based on digital (67, 166, 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, 68+98, 296)-Net in Base 3 — Upper bound on s
There is no (68, 166, 297)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3166, 297, S3, 98), but
- 3 times code embedding in larger space [i] would yield OA(3169, 300, S3, 98), but
- the linear programming bound shows that M ≥ 3 145566 905206 556561 079117 444018 998166 948051 499966 031118 572360 494794 367484 862757 762442 210904 750793 628847 845204 564345 450574 808528 394311 451086 841320 852793 352242 295963 034606 687877 000719 167652 434469 563763 919442 099435 156360 921106 773313 644723 815840 069970 516352 488061 537209 126970 391505 512852 173558 511692 761097 990870 417317 392643 532114 873815 687941 721131 733105 825583 890352 351839 001994 824941 940256 785712 216786 653363 457886 734147 767037 736609 039838 841225 726331 561823 957069 404686 908950 493421 943863 101500 453132 060360 838805 446486 663874 725827 416515 524411 804410 200448 670746 574506 760642 871953 011182 748669 236423 946743 270142 297205 308577 990731 097631 287588 443080 522918 253237 153550 097076 225657 009426 778628 735219 609626 932775 404209 334352 834835 681478 858199 841492 251445 092508 326966 872363 680773 591740 875850 214106 392603 163110 417985 347972 412230 751067 375249 320021 343954 485330 331247 350736 888856 017263 795395 225836 287088 949376 094163 391000 689893 787626 917874 039320 869009 987682 273511 272847 583578 185661 538804 160108 749881 608496 / 6630 227894 565886 783255 969340 362479 203729 263367 352926 647580 077799 287525 939848 062690 330582 487464 258273 260235 557199 731533 290631 851538 339812 814032 777259 274026 470574 144587 351153 934938 207615 856867 829377 820514 772681 496380 183600 612036 954139 815987 398154 578201 017174 792036 696947 885233 647174 575184 659844 723029 884327 888989 605389 053165 579642 512142 454313 146964 406382 726297 901980 480388 539617 680284 015798 657656 677881 600502 074319 235144 391625 101426 701162 228765 491761 001269 067573 513197 945955 378278 026978 231526 483189 816511 420438 768021 877301 386814 283567 700126 436081 443052 503571 064869 802708 900446 643492 195718 088210 184796 135546 968173 636466 654503 772226 066966 929133 084720 590801 146089 153886 922619 713282 550346 419446 260245 535151 169542 171283 368223 458888 716707 673821 423405 300702 864923 404217 653870 178304 433862 237888 900185 613338 079992 823413 491448 223580 424433 495966 946362 798189 051239 456201 785732 837084 258379 003470 108168 196238 314540 398325 > 3169 [i]
- 3 times code embedding in larger space [i] would yield OA(3169, 300, S3, 98), but