Information on Result #1880928
There is no digital (15, 15+k, 410)-net over F25 for arbitrarily large k, because logical equivalence would yield (15, m, 410)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (15, 817, 410)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25817, 410, S25, 2, 802), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 114550 011750 986939 503588 951487 361734 510289 009611 658681 972378 791085 207155 155444 856449 212566 151397 924042 800105 416263 404572 404053 239384 309832 274004 148520 646169 785205 612185 520401 620005 301194 513657 872477 985949 817432 375432 147184 509215 555259 552096 504609 736328 372915 931240 499788 544772 751233 940482 414639 190599 961412 894919 480630 795498 786335 835048 628312 498564 197214 472302 465252 673285 625034 782534 363374 206480 792235 440985 466877 914691 098897 896700 075392 713606 197997 305461 265362 674919 056077 960368 508963 507060 020385 483100 258473 503358 673814 302436 709333 367355 921267 920401 388553 017108 657440 753861 181136 013955 975953 097594 345784 571494 500295 000821 418667 980833 744301 704514 498042 863110 958759 526719 319702 163433 475232 638400 877456 791409 067890 067355 142897 235145 470459 252422 639159 007462 183566 241077 317506 190234 837755 819469 583153 375695 886526 151056 189696 586853 157588 591380 758764 161423 267813 993708 627322 600427 270697 099242 552005 070488 293354 515793 757010 134271 728298 983584 238607 569974 352967 552522 904709 828638 666252 012542 717899 141901 147171 687069 810643 044291 849011 134737 945479 823920 311727 074195 301440 217347 805561 105717 406372 450007 145134 535826 817845 372005 422177 608124 911785 125732 421875 / 803 > 25817 [i]
- extracting embedded OOA [i] would yield OOA(25817, 410, S25, 2, 802), 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.