Best Known (93, 93+∞, s)-Nets in Base 8
(93, 93+∞, 194)-Net over F8 — Constructive and digital
Digital (93, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 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
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
(93, 93+∞, 195)-Net over F8 — Digital
Digital (93, m, 195)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 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
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
(93, 93+∞, 676)-Net in Base 8 — Upper bound on s
There is no (93, m, 677)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (93, 2027, 677)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82027, 677, S8, 3, 1934), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7874 915450 608252 625049 320331 959380 639792 380416 632502 984202 712403 309546 396370 835268 447377 823685 711863 778289 397260 691452 213571 637996 019718 550810 622563 080176 178370 455007 701369 553569 322382 363930 834278 480047 548597 479948 709716 645076 882402 530208 595069 760589 918308 350927 358498 984406 929032 986751 458127 133638 158790 790403 167609 898376 686343 953563 651466 018483 454375 971496 679366 675940 127751 208617 238238 968627 254391 939445 444994 061026 219518 581889 269384 129758 687909 703412 941616 852501 480046 013897 424926 115193 038459 476885 995605 769307 519550 556814 965270 087865 469697 308244 168820 248069 244702 110978 059747 561779 209977 662652 320533 577236 230186 461529 836972 698007 664874 377272 959918 891148 605504 901406 931083 502485 000158 672939 752726 033055 520322 108718 439146 253127 635859 024377 021240 960581 606528 647180 799564 207222 157806 310681 986912 031659 048787 727395 550080 823277 569333 886443 160233 446085 458778 858022 824593 000959 870119 838984 848212 743465 453371 345718 396232 924931 476729 969772 577887 551274 601084 781922 480999 309456 141744 263720 051101 444189 679526 416043 592536 579151 503170 410801 513346 206307 155810 033060 510934 056951 333392 936811 794964 049914 404399 700812 929953 412790 434448 401130 254255 233544 986219 181719 963220 062402 845176 003235 559299 490505 688429 131756 405996 445767 560703 554396 931549 525904 695835 477212 308709 094825 165050 799260 893726 992372 705861 947551 578936 136304 460635 457670 779671 457506 996314 044079 313251 250815 014353 273479 283461 022490 507414 995640 951030 245906 510939 312479 913044 434817 836810 262532 784343 771231 672446 102017 155110 467335 714885 975194 985185 925085 870323 965534 564071 447459 003375 515219 093737 198057 371858 490198 381865 746288 357833 987910 475221 698139 635607 621040 142903 370516 605313 599343 372522 614778 172783 757834 164310 366969 960753 298791 614706 089308 171313 976517 221339 717381 220702 898213 220394 696829 672637 105290 841092 207441 759209 349237 474707 038344 074881 811069 255326 713646 297884 518131 354518 421504 / 1935 > 82027 [i]
- extracting embedded OOA [i] would yield OOA(82027, 677, S8, 3, 1934), but