Best Known (100, s)-Sequences in Base 8
(100, 193)-Sequence over F8 — Constructive and digital
Digital (100, 193)-sequence over F8, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 85 and N(F) ≥ 194, using
(100, 194)-Sequence over F8 — Digital
Digital (100, 194)-sequence over F8, using
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 77 and N(F) ≥ 195, using
(100, 724)-Sequence in Base 8 — Upper bound on s
There is no (100, 725)-sequence in base 8, because
- net from sequence [i] would yield (100, m, 726)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (100, 2174, 726)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82174, 726, S8, 3, 2074), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 43553 493756 233650 600228 025024 909154 401241 032330 020878 504512 854281 528925 838864 219760 442468 731438 882650 764842 573466 729452 249846 826820 972444 351802 457363 331681 556424 377675 790441 648284 247602 845727 468056 964726 523437 502960 314620 845865 276933 275394 591296 614765 274846 675372 894586 939377 939032 442255 281298 928901 259115 677295 665870 554321 053665 920762 039653 518242 231845 552690 702666 579381 087739 078841 794191 622017 074048 113932 232739 051150 352501 144703 484220 921836 808895 067994 698594 251555 438878 106873 584659 563713 342620 800455 456132 770668 391848 905266 784018 416948 822167 589552 510358 386515 161957 027522 310444 222697 865942 191107 561649 609745 615228 414626 590532 009273 737275 978097 600613 996046 197659 630428 458958 591979 532873 327858 352901 535142 441839 970555 533751 620939 111383 025760 410862 062495 196002 235555 589162 185549 540852 671435 361334 838988 015266 061566 503045 258789 527949 084111 359963 197609 177102 048846 864281 967879 213352 086863 411872 774782 329282 204617 725794 764127 681188 002039 677170 487759 018362 099860 192574 356657 908956 959125 873959 003686 720046 650385 084869 685159 650754 300306 175880 776811 757462 618912 651661 236848 641347 151592 641150 240043 432768 977550 051825 981183 209903 714349 847308 022771 224943 713169 079390 857783 661224 051734 421521 339519 734750 072770 297902 520151 429431 468514 836087 745513 848883 496007 549579 116526 800755 608461 564469 155033 174033 218287 766743 455078 590091 174778 953926 344101 038587 988376 719074 253187 942764 098034 086333 041872 663604 987038 447702 829830 988407 888629 081742 126291 450816 702640 804635 150298 986764 531797 636837 712223 024572 526253 722097 773247 153467 270123 647212 102464 058898 125045 924364 862514 064557 573339 845620 631387 415430 485991 241627 643319 786439 003751 799259 229021 973113 230694 442140 154983 011993 585721 522037 929569 168437 054799 832139 154628 249270 536796 655961 123884 648691 722488 491366 680799 246469 910232 064356 186210 690319 359576 900638 599737 354328 055922 015550 395514 264426 571022 013398 571051 853390 553830 440023 509379 139150 302886 717672 182074 357049 931128 946821 945918 624362 999141 940640 552196 220941 940848 735272 338531 201459 421184 / 2075 > 82174 [i]
- extracting embedded OOA [i] would yield OOA(82174, 726, S8, 3, 2074), but
- m-reduction [i] would yield (100, 2174, 726)-net in base 8, but