Best Known (97, s)-Sequences in Base 5
(97, 81)-Sequence over F5 — Constructive and digital
Digital (97, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
(97, 159)-Sequence over F5 — Digital
Digital (97, 159)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 97 and N(F) ≥ 160, using
(97, 405)-Sequence in Base 5 — Upper bound on s
There is no (97, 406)-sequence in base 5, because
- net from sequence [i] would yield (97, m, 407)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (97, 1623, 407)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51623, 407, S5, 4, 1526), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4919 864093 270274 258395 972192 064278 711182 021957 044368 680534 368996 588517 778817 990927 138934 406882 805832 991613 944717 156290 919545 421689 890138 222540 451548 256799 517101 548651 910405 839086 965969 292318 712884 595079 294741 671559 589070 756118 774787 540771 918080 500090 296362 147461 443399 375249 595210 939966 264603 511421 827462 703681 588591 645485 120902 319714 051989 584395 475865 917303 662269 905901 957048 351034 819889 249575 900979 247612 099009 880613 055142 242372 921363 792561 704920 796728 089967 247558 397785 890986 304984 749446 995673 260300 907649 875468 596170 149185 158269 846185 062178 269100 594860 495114 693752 627980 235744 041500 887704 112194 369817 212370 766304 784419 279509 345890 419174 689710 878226 341977 143221 657167 695325 557786 926566 883128 246509 175070 383884 072049 440176 219902 348452 840083 936820 236374 439803 618505 918232 841867 402732 267314 654297 794721 545111 270831 557089 999418 527022 520382 813735 959082 989192 073296 874493 354493 871056 701196 816569 591032 007377 025585 305169 653090 330247 838219 751490 586703 648187 431997 546031 221860 690272 781294 817568 941796 524150 433985 637874 073278 769279 220174 125464 557904 896515 374662 764324 988022 976469 978059 136806 173450 546879 853673 143401 238121 441565 454006 195068 359375 / 1527 > 51623 [i]
- extracting embedded OOA [i] would yield OOA(51623, 407, S5, 4, 1526), but
- m-reduction [i] would yield (97, 1623, 407)-net in base 5, but