Best Known (49, 49+∞, s)-Nets in Base 16
(49, 49+∞, 243)-Net over F16 — Constructive and digital
Digital (49, m, 243)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (49, 242)-sequence over F16, using
- t-expansion [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
- t-expansion [i] based on digital (48, 242)-sequence over F16, using
(49, 49+∞, 773)-Net in Base 16 — Upper bound on s
There is no (49, m, 774)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (49, 1545, 774)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161545, 774, S16, 2, 1496), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1261 746483 725441 291961 499930 928796 093723 197592 699335 887255 140033 581193 677430 024070 178965 625826 497593 980142 614769 471188 263198 179609 382314 258323 152422 616912 702087 384294 290615 715417 123786 026823 425927 260740 043693 513162 756514 470446 440584 412210 789496 259061 005977 782832 736842 056588 055588 437450 523149 599643 740321 122357 657219 130859 447514 990848 525663 731781 297130 770051 604593 087374 078506 645958 623529 495513 484090 639953 895054 013434 335589 465304 057137 507996 615147 626564 427094 380960 878387 957248 065776 174765 690762 410452 046140 948753 928851 735361 342929 967498 309136 211700 492434 993265 005261 856463 795680 728378 078147 222121 941858 122419 879680 327290 577455 833484 957373 379838 914793 013402 095792 269502 064853 005107 363466 470189 868869 297010 007753 508973 425767 554149 533892 657404 745384 697147 821167 863323 215927 476121 343374 374738 555578 807836 843950 300789 363060 518059 822712 639109 503255 338829 073760 561627 382385 174906 664521 574404 710846 312509 556063 511782 830951 243989 876924 103835 051163 597992 167888 704863 097320 375836 292927 026516 468365 358404 452466 594132 484314 051060 792258 718671 826168 847765 587368 631206 887757 530084 105753 690411 928113 205986 536179 195592 541384 234326 208179 273034 918289 700652 905740 948123 508804 586736 740930 782329 404545 073336 092194 778694 937937 658970 245164 431131 363597 954209 543146 748966 800556 280450 306076 795154 762898 140128 607753 924761 543936 711489 524674 749477 465419 077677 013701 752557 907890 593004 070714 372222 559750 019680 265538 851771 429016 558144 984028 202655 607265 407031 883570 029728 342844 192531 813169 362599 242057 468307 578143 229978 723911 817475 851890 261319 555443 814686 077574 868444 543594 463792 242842 288975 161321 944520 386069 171735 384101 522309 102324 797853 329098 683302 686215 477477 592230 612928 196936 357004 437943 931189 177315 578763 243728 467371 439782 584816 139737 409055 481962 838065 341551 833217 592147 387083 659342 678973 324807 826209 107694 628098 793826 536120 880981 842077 611428 333498 581522 400940 334591 449138 611975 166565 023744 / 499 > 161545 [i]
- extracting embedded OOA [i] would yield OOA(161545, 774, S16, 2, 1496), but