Best Known (5, s)-Sequences in Base 128
(5, 215)-Sequence over F128 — Constructive and digital
Digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
(5, 226)-Sequence over F128 — Digital
Digital (5, 226)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 227, using
(5, 773)-Sequence in Base 128 — Upper bound on s
There is no (5, 774)-sequence in base 128, because
- net from sequence [i] would yield (5, m, 775)-net in base 128 for arbitrarily large m, but
- m-reduction [i] would yield (5, 773, 775)-net in base 128, but
- extracting embedded OOA [i] would yield OA(128773, 775, S128, 768), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 669290 325627 546458 184620 213577 545087 276951 806862 282307 494737 114444 198220 640996 638439 036610 024307 196628 286132 127525 860996 692440 133799 083107 714654 194007 203622 021144 548531 650151 200958 572936 404927 009197 949729 935700 307161 548321 102872 326218 830784 109246 789244 660536 796528 040523 275170 011751 802865 395598 529426 681984 555555 943015 922137 785437 824055 233960 074970 215157 509839 308694 746154 926115 511795 250359 263688 524153 252405 804485 610504 200714 314498 028893 688742 083416 935789 844751 092803 131119 547124 166857 669164 423068 317017 987076 868902 811591 845252 742984 932047 842793 310322 324794 725538 314820 884377 522052 902674 139027 507787 131906 728569 458060 730448 498827 732441 684991 578738 528563 326668 963501 280898 873930 437062 314037 038568 318879 590364 824219 315076 464438 454394 606653 076011 148457 442269 664370 642189 753223 943427 862660 741290 483301 768582 619665 143251 323143 948906 724768 001162 839852 425518 221049 530195 613144 592187 828670 767499 868624 571652 928025 573491 342281 009171 517424 612312 680308 194349 521661 314101 359233 633146 233540 364628 158671 195419 250350 318879 707018 808738 045837 926626 320153 784940 637027 193854 993763 333171 525501 084027 627381 086996 587999 986610 493395 525055 163721 821309 000707 524076 433022 662235 390758 802701 163321 228686 968638 530046 882080 318698 945260 761318 293819 163423 690262 604603 654771 599527 638473 462288 918667 949391 835693 223694 939371 745177 698502 931977 492347 799976 983045 744310 862603 788143 656491 286311 711589 340388 137468 939934 501245 992302 572744 526600 846649 237233 137339 588928 262955 099573 532946 976818 621147 655568 891809 403534 889629 675716 993881 915360 830936 022928 592142 857937 375823 669465 418196 208943 518512 186543 569695 412591 746759 644245 789221 513056 745508 374998 356979 550641 469163 307008 / 769 > 128773 [i]
- extracting embedded OOA [i] would yield OA(128773, 775, S128, 768), but
- m-reduction [i] would yield (5, 773, 775)-net in base 128, but