Best Known (115, s)-Sequences in Base 8
(115, 193)-Sequence over F8 — Constructive and digital
Digital (115, 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
(115, 194)-Sequence over F8 — Digital
Digital (115, 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
(115, 830)-Sequence in Base 8 — Upper bound on s
There is no (115, 831)-sequence in base 8, because
- net from sequence [i] would yield (115, m, 832)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (115, 2492, 832)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82492, 832, S8, 3, 2377), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4050 023596 832501 633900 295555 335147 103061 700103 347150 588825 323203 156134 197911 784803 533339 255088 155402 780672 900046 636048 719505 097434 891983 664443 420511 051176 661725 685000 445996 670887 118488 433444 348064 969500 759893 259379 756841 957838 751486 821747 553495 533653 158245 885468 308672 800638 925682 595554 049136 520023 274212 651077 987166 486982 443315 715383 868124 773810 835020 978237 718894 488425 402681 473704 667668 377691 134486 711687 500708 777074 707469 822338 090236 135976 133169 678706 249438 193867 994206 390227 432293 958121 776285 089593 267068 552370 432380 780087 792333 761337 800299 296527 809102 708399 438469 791192 235241 055382 543271 920707 096142 752660 119553 671806 148766 295932 204424 695643 036627 254430 654734 932098 021725 858058 943988 750420 271818 650360 116035 481252 720235 739807 973869 355452 746271 535526 183361 118019 671353 196395 503754 984097 519027 631135 235072 784050 802113 505111 452098 034629 646791 857713 729100 092563 798844 984369 755086 860187 669614 088551 134286 083364 994472 765619 003086 881362 431971 363344 353640 663563 535464 706026 025368 774565 194238 415161 912390 354243 971881 132675 964880 955536 852298 844613 052849 312041 948705 660456 763025 225335 242230 138670 150675 015556 171637 550329 482076 104487 753455 179554 519444 886562 711750 035886 526083 399393 064520 267000 981962 706080 304643 315567 687688 702583 700729 484396 765765 143365 305118 478106 972081 918110 842964 847865 200029 758261 265757 050114 130425 264431 705857 668005 188666 120744 468627 129760 190205 528560 237651 495353 755789 998551 440891 773034 893845 186153 361220 933287 380747 566677 407530 005135 116379 949507 732572 363299 000005 990613 053708 350936 120403 820664 505614 848910 125290 667127 465389 739442 629687 824782 731376 829258 462480 767338 566475 736978 178590 578211 162767 629329 481969 416312 999054 073010 777253 894041 904666 391632 436355 231563 750973 845955 056263 384980 048749 138345 481630 492535 420454 735160 132406 283234 458471 584075 994564 507177 693894 162219 826203 921487 870450 751266 892283 397573 601535 945688 939185 913765 605088 631957 650231 905329 385972 136846 296425 792418 681883 655164 187820 234396 431926 650877 778524 201494 856909 186043 722790 257161 445706 823888 967509 754814 855600 712398 192902 296229 014402 319764 445464 243107 254523 074224 170593 388594 337085 315825 514099 065234 913458 496485 031961 276974 689515 057592 334223 818614 632216 358937 569675 136502 389934 767906 019880 359833 026229 721089 174334 740004 345468 799056 187328 036363 571044 357712 723920 814080 / 1189 > 82492 [i]
- extracting embedded OOA [i] would yield OOA(82492, 832, S8, 3, 2377), but
- m-reduction [i] would yield (115, 2492, 832)-net in base 8, but