Information on Result #1879338
There is no digital (259, 259+k, 796)-net over F4 for arbitrarily large k, because logical equivalence would yield (259, m, 796)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (259, 3974, 796)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43974, 796, S4, 5, 3715), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 42 442232 731241 347711 832621 168865 740061 833805 520958 623614 256181 067713 982996 082180 257158 837253 935277 316464 150531 767198 417162 567207 701497 574696 174298 388902 371340 170370 677660 851975 740753 931503 498555 032172 271212 096595 029227 789413 865159 724991 280278 989113 841561 776704 137996 185188 614627 495825 689661 975766 182563 838269 413134 415488 801213 704665 160798 803900 287880 529287 079439 324756 435275 780017 664637 828352 948848 824522 998021 764479 870380 311142 907603 895932 604298 161004 276225 682606 919485 459806 884744 896594 246330 998582 269642 265311 729888 055290 927575 676392 429333 294692 505344 473657 743312 902992 756134 833538 735244 937105 464662 225385 510529 592851 273236 313309 067738 545031 742285 920473 287627 784584 587726 863734 274752 908244 176524 826208 862111 696800 728123 446745 165506 616303 642152 983542 055784 783965 106085 042718 254336 392498 939518 104173 528478 584665 149400 217268 948039 014026 757141 680768 294055 728179 656948 397480 741726 792745 540852 927936 455489 455927 469953 753450 335243 483499 472809 582495 368298 179243 588046 231103 785764 196404 046182 093310 850272 693017 551238 316349 198682 116475 278013 815951 333278 643650 260432 338048 134766 568527 279796 267583 817645 803433 722967 559801 169692 050003 947485 466097 392303 923689 868769 168544 762027 943274 194565 368026 313967 627555 359027 554369 402534 530246 489963 240887 279193 673622 628864 862533 749081 145911 577392 512537 476182 793382 586304 980740 963063 079176 859922 172625 207063 923568 183844 520470 896270 935867 213234 096938 551567 974246 960748 351406 496457 362563 711500 608946 977010 599739 321211 728634 569168 155965 561642 038445 258898 553075 814135 554190 421993 960073 012077 336011 677088 861062 165240 978208 113618 670848 410986 082680 363855 716538 298123 548249 972491 220168 368310 452758 934814 867066 663074 729405 097556 109443 743952 490623 195578 748811 258862 989193 211217 217681 332801 845920 194840 944815 490916 095041 814556 909995 745825 744591 773793 340819 678397 158223 053797 550232 160767 130171 962316 670024 791484 247656 811456 608679 540353 068316 123774 038045 472034 303517 876535 063741 240351 103575 646610 458391 905363 012242 627477 802828 192001 622040 117457 245778 705751 304411 881351 435975 813653 503786 427880 137393 985964 358745 515252 700131 586310 537671 067741 107265 676518 659665 471371 904756 475121 100925 113167 550820 729659 560632 634640 615210 392096 381064 660286 823187 989543 916895 087731 859070 036692 667797 407054 246251 984232 761505 256568 794240 596134 841072 192969 068407 559529 345461 090338 055094 248554 736473 046285 232682 877961 057344 158265 906287 728459 689095 434217 757209 961977 347127 095940 697213 219849 549290 826996 121600 / 929 > 43974 [i]
- extracting embedded OOA [i] would yield OOA(43974, 796, S4, 5, 3715), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.