Information on Result #1874723
There is no digital (73, m, 309)-net over F5 with m > ∞, because logical equivalence would yield (73, 309)-sequence in base 5, but
- net from sequence [i] would yield (73, m, 310)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (73, 1235, 310)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51235, 310, S5, 4, 1162), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 198 606391 890078 266161 670144 321766 233874 518209 541395 727622 158425 196952 706160 496451 434713 971813 306799 268005 662428 417619 992962 950191 107435 098477 210136 153184 878793 148957 460919 072948 991008 210581 481325 424307 980961 062711 890541 348053 833933 549446 913210 445577 449282 143765 911064 093790 823696 131129 577007 393667 298542 438996 399671 822029 410802 455868 119238 392580 234319 631420 417335 007117 789256 415248 080070 534118 217085 935297 114271 219165 468163 385371 302365 459615 821086 048530 873271 198841 244956 069676 583810 455275 765376 991002 452076 205987 725913 777897 614767 391838 474121 695360 791447 202499 054754 266807 951138 791528 037743 445211 950962 146686 833487 686730 670313 874112 164307 921496 878501 231818 938730 632881 929388 167747 609438 271754 752097 821611 195429 305548 052604 566495 931152 774895 337115 053380 639334 958757 379670 308757 222553 907897 766221 111904 281088 038745 235761 076200 591002 116624 395057 442598 044872 283935 546875 / 1163 > 51235 [i]
- extracting embedded OOA [i] would yield OOA(51235, 310, S5, 4, 1162), but
- m-reduction [i] would yield (73, 1235, 310)-net in base 5, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.