Information on Result #1853781
There is no (23, m, 603)-net in base 25 for arbitrarily large m, because m-reduction would yield (23, 1203, 603)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251203, 603, S25, 2, 1180), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 69830 686364 467775 771116 795941 629618 640090 640956 151459 688048 129159 313692 466635 754942 309059 132953 841327 351683 894745 977836 366397 258213 660125 969338 011177 941159 499293 597131 803306 594659 544394 026490 373937 120115 704224 665345 061921 222395 952890 950887 434412 386660 638923 584428 295591 176704 205807 911592 084047 067631 448528 696410 921009 550097 603824 086060 881198 818357 569459 058003 057858 650152 169626 397766 075050 312462 395568 535920 069012 675049 664648 326351 119890 054190 163021 246250 496256 271269 189932 289856 406856 464632 065814 507860 631745 685087 758463 377754 332906 409509 044101 300453 727191 944771 098250 208354 773014 891423 701161 464849 933144 504131 732511 362607 019111 608923 573059 115274 466793 792219 047227 660250 615024 470432 824644 693946 957912 853367 750707 572560 222199 962832 072042 993537 127754 124458 240843 901521 053733 389114 586352 316687 307252 094743 125637 213764 705783 728625 174058 476541 565383 135524 265783 464439 246799 870723 054488 808344 923632 206636 104443 471588 647815 444395 099701 796267 691033 830214 279265 162052 904448 683272 942332 622184 422554 040335 190952 765813 288402 282277 217865 028582 214680 768636 634817 379246 041555 515917 990493 598969 511888 038243 288779 189412 034773 430739 501633 956232 981247 749897 037744 675260 387633 079683 413942 777891 103269 756391 988618 530630 788808 983768 369225 660554 027161 253897 824069 098527 122440 396074 190948 266460 827434 800689 254019 217062 408183 724548 267548 376758 926162 869079 752556 623170 096516 559062 026663 807982 194579 906361 380799 228518 162330 905648 241361 236821 544615 637905 554078 008543 960660 324894 197172 163344 796161 257185 928646 410826 681486 263910 079774 375826 114013 985651 537817 117105 370755 315930 645436 250975 814631 840420 959050 216225 158305 244594 301817 760028 575407 802518 221980 333354 865612 277844 084954 114833 863059 175200 760364 532470 703125 / 1181 > 251203 [i]
Mode: Bound.
Optimality
Show details for fixed 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 (23, 602)-sequence in base 25 | [i] | Net from Sequence | |
| 2 | No (23, 23+k, 603)-net in base 25 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (23, m, 603)-net in base 25 with unbounded m | [i] | ||
| 4 | No digital (23, 23+k, 603)-net over F25 for arbitrarily large k | [i] | ||
| 5 | No digital (23, m, 603)-net over F25 with unbounded m | [i] | ||