Information on Result #600016
There is no digital (12, 98, 1438)-net over F32, because extracting embedded orthogonal array would yield linear OA(3298, 1438, F32, 86) (dual of [1438, 1340, 87]-code), but
- the Johnson bound shows that N ≤ 7 873843 801320 130345 127812 803797 692188 325490 978622 971317 871877 255072 656728 253760 668749 371449 370536 154355 287098 271319 118519 869973 021535 550467 807275 117173 858056 787996 862675 555931 381663 285617 621776 482362 417815 348381 434499 771596 662366 141496 889889 669893 527005 255819 043147 010860 257918 558957 577353 607336 443439 861191 623223 150090 142136 097223 767096 019204 774514 604665 180644 174849 827826 886185 740989 392274 137422 541769 799317 984682 517655 264667 499454 854744 009525 465572 527018 032719 571591 289438 688291 903082 830645 444797 791708 796481 802317 113317 351213 709870 681299 895387 989515 496234 589510 591715 856828 507883 757216 469994 773615 336452 115173 384549 904809 149019 395389 171711 632552 453646 720446 819257 059207 030445 788366 940707 375965 360792 042235 914062 010691 764737 688766 685092 218077 104319 123739 519865 211116 771776 226827 876921 122054 861457 725591 004901 031231 743911 728943 977604 451683 092490 147761 955188 166882 325060 823936 105511 183006 813118 776812 590002 878412 248674 338638 836919 226478 457365 695252 446247 952604 912719 257452 091061 310133 088121 953072 764248 466194 003074 352326 488020 665748 080670 153773 223440 762207 218625 260794 678322 691906 005534 331133 499488 805949 722072 759505 182992 705033 363110 474641 775287 869746 869190 888033 697174 888955 036524 371550 789201 446553 661459 464671 823544 829458 116315 238468 792045 053826 547615 801747 843659 983617 101112 866974 842743 459258 461367 248471 369089 940591 893578 058082 481536 139300 515945 633267 334713 186936 525862 292916 977653 795246 200957 831796 241022 965696 671461 179154 874971 029216 904265 883406 024290 972314 212650 859616 368336 481741 353832 447919 601110 278820 190480 432670 971629 651436 563901 511478 263245 388717 229533 694106 291400 195567 120039 264363 513696 664179 063913 702303 683544 642329 267810 917638 732193 252439 670351 070390 586808 454957 390245 190797 302853 768711 666246 224436 930171 203685 475307 368361 102870 087329 858856 709719 102332 966260 364330 138782 895332 064759 659380 052136 499585 762970 898910 346652 845101 678399 585178 734244 827915 712372 326047 444004 118652 070866 446169 519926 004926 482827 528932 414208 444150 603217 787750 880569 913839 602385 843897 264410 017427 160221 773702 675085 815876 338314 < 321340 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (12, 99, 1438)-net over F32 | [i] | m-Reduction | |