Best Known (116, 116+∞, s)-Nets in Base 8
(116, 116+∞, 194)-Net over F8 — Constructive and digital
Digital (116, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (116, 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
(116, 116+∞, 195)-Net over F8 — Digital
Digital (116, m, 195)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (116, 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
(116, 116+∞, 838)-Net in Base 8 — Upper bound on s
There is no (116, m, 839)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (116, 2513, 839)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82513, 839, S8, 3, 2397), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3385 285491 741187 444421 293876 243000 687403 771906 118176 371585 610199 442747 559146 661159 428541 744906 441695 726670 203695 758916 949851 316251 033847 647204 745232 137983 266574 836415 301973 376554 851509 884986 056454 895834 652864 017600 158161 643240 354005 542520 123391 312541 153086 966820 905194 720770 438604 858519 894401 320419 933792 810003 447669 740705 139160 972795 564896 558247 556358 603420 692723 354627 328429 528381 377032 624934 445983 397483 254899 961454 110067 376735 523504 927280 744497 841644 260350 242071 086612 468241 050869 982376 805593 165065 486364 759909 078828 303231 173836 808527 275873 321185 787082 171407 790739 979228 491141 116506 845354 635939 438792 386311 293730 332532 306422 810908 664849 125232 779427 449172 982024 787469 382090 988994 150403 983827 532064 267868 110091 243925 708440 410786 648334 585695 394249 821407 081333 299454 894322 721862 131057 593482 602035 843469 790014 243883 672491 106121 022496 719872 281214 485238 159053 299655 879884 647715 291741 486237 225919 202913 194021 087552 338723 873627 592923 717660 081133 452931 515760 227726 375043 630272 109651 264352 889444 963206 242981 813929 624547 961944 896970 458769 371058 161055 562543 632486 090895 862501 959255 103073 328562 517095 037890 887854 086463 836871 232452 453968 800460 169369 804940 303542 153880 739840 980433 406423 450180 192544 252563 359162 768207 837403 710017 537295 414446 073614 277764 081636 594168 239286 387948 715683 883495 173296 808636 369001 120760 717762 838684 326339 810011 416375 961456 945706 358217 736050 233144 946676 166279 248916 891496 844578 556431 630989 804001 969353 405078 649179 567380 185458 031880 484691 759072 343150 515616 103895 695291 879611 658186 566362 129067 130915 995634 433935 009554 843986 437155 002410 273710 847035 391340 459163 412842 474217 566426 107963 142437 549642 611838 780819 889986 442976 403698 465184 556016 755796 979944 083699 704572 983900 628953 803534 268172 318026 614265 191310 625862 659055 842127 620348 032599 969309 387559 744651 465921 939768 351444 911956 923840 446922 417644 534884 015329 334375 739855 027025 698109 989028 747072 896396 499626 737545 654826 184269 038089 586893 353447 385735 661348 303418 693549 927699 353630 324199 732051 932061 816196 485722 832358 600659 431830 344599 223022 815142 163953 165342 297591 310393 192501 454245 644862 901995 026903 108051 279941 602539 057807 291905 008770 711836 221162 618301 578563 187953 601974 256452 660370 770524 787978 132567 791365 580055 519841 948056 858526 868764 811274 611927 244480 699912 750709 197392 827117 552772 094556 962141 734382 775732 011008 / 109 > 82513 [i]
- extracting embedded OOA [i] would yield OOA(82513, 839, S8, 3, 2397), but