Best Known (43, 43+∞, s)-Nets in Base 16
(43, 43+∞, 225)-Net over F16 — Constructive and digital
Digital (43, m, 225)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 224)-sequence over F16, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
(43, 43+∞, 226)-Net over F16 — Digital
Digital (43, m, 226)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 225)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 43 and N(F) ≥ 226, using
(43, 43+∞, 682)-Net in Base 16 — Upper bound on s
There is no (43, m, 683)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (43, 1363, 683)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161363, 683, S16, 2, 1320), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 391650 610002 786258 566814 689116 747969 770218 122594 620257 658947 250081 160158 062601 302159 410143 194519 505247 174097 807024 650680 029947 461527 298583 773843 572590 868715 834642 965351 525687 307548 065917 757954 632386 541353 231119 681760 515850 379972 019587 403535 513233 207231 019528 071526 593608 165412 231749 188907 959770 574146 099570 877463 572132 718557 306956 617706 381787 517271 562853 289422 859377 240407 781273 629006 446914 253267 652505 179345 569703 774325 489267 315705 933172 040365 098976 663100 729392 204226 957991 879164 170084 106875 123291 307798 924262 766942 945117 601650 605546 847703 134231 041445 474224 414035 497981 341215 379772 900158 391992 661854 177235 039057 038467 753674 000666 001105 496221 282644 867743 388723 591496 374303 491148 025862 472085 831103 172047 617262 358879 981491 465506 053899 846380 716244 089717 088009 485715 357450 086592 058792 237786 868736 937857 452294 211364 182884 009225 974394 291957 087767 163697 695351 773336 179380 620684 991050 096383 524372 545315 124017 110331 023357 470417 215592 708103 312151 662787 031879 430263 784927 896319 284852 630421 681719 048768 977974 897179 195501 418819 199195 405872 830022 041904 212232 863573 225952 515515 993546 464116 007478 124691 785992 357901 175745 701844 137815 091081 915272 210005 781632 151147 308381 577492 281403 709954 292184 952013 455011 797405 605398 013001 000493 039321 455101 233785 840993 164270 030474 919154 637736 469425 062705 736069 978647 135966 113806 117767 829314 863945 253444 031522 869614 894606 761809 620693 704104 387750 016956 186296 373763 080066 362014 593905 103057 747152 448402 925773 641062 953604 424499 309965 297356 455896 891553 344880 163572 417971 683060 637629 783122 426612 790150 779018 218637 634644 696218 681883 126362 030807 881802 693156 583610 632071 578758 871731 033754 794646 953706 023337 711583 777050 326340 696251 826176 / 1321 > 161363 [i]
- extracting embedded OOA [i] would yield OOA(161363, 683, S16, 2, 1320), but