Best Known (22, 22+∞, s)-Nets in Base 49
(22, 22+∞, 344)-Net over F49 — Constructive and digital
Digital (22, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 343)-sequence over F49, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
(22, 22+∞, 1150)-Net in Base 49 — Upper bound on s
There is no (22, m, 1151)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (22, 1149, 1151)-net in base 49, but
- extracting embedded OOA [i] would yield OA(491149, 1151, S49, 1127), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 531486 249207 715949 199721 396585 411646 184951 593361 460730 219156 605868 223494 175378 554732 751490 922012 974073 912154 225573 504494 550845 201190 235130 512320 485779 399915 026854 825966 579441 103078 392684 582492 121716 869593 304756 129050 156451 215703 282564 344977 260359 287617 471834 150388 676194 247288 510985 573629 659939 446279 711875 167612 838916 744149 859282 095272 896973 383897 603219 437589 053632 596274 915938 903715 925565 059939 997980 504735 832566 709643 494969 510724 565039 437023 705089 435937 810069 303265 294751 952801 811634 078670 589369 083810 573363 743104 345921 658530 669628 010153 047621 462603 295251 667145 076505 093500 879456 757590 876388 626288 328716 653197 573202 647056 320323 892443 781168 018769 294566 226157 122343 803177 382186 265727 658656 564221 429170 565160 632076 560851 985722 258228 210355 762750 286665 061286 703008 902144 011588 986305 602143 246189 571173 845732 790230 496238 387204 735255 728860 346736 885329 001233 825792 443263 637359 338918 352177 945746 568651 715278 486346 464937 055908 450766 779691 696500 131659 084650 131978 301159 980220 875077 987109 947373 612953 559001 636075 667022 230553 603545 089299 321206 334364 711924 195013 259058 360164 043138 665727 811086 442976 996803 558646 418135 444211 382666 078815 802033 274922 739794 757221 572596 191874 504262 586774 963492 165066 874140 005247 454107 382749 121980 671998 651938 589281 458955 596837 533626 282467 966924 730860 319934 473581 593233 892434 630128 230739 233821 510704 625786 406934 287239 644970 953955 060578 435592 025274 454270 059976 083101 490612 421783 872870 831939 134637 870372 177676 462469 889516 807839 526779 139868 314223 514767 444428 780089 711467 830636 601821 859690 704247 050946 685431 972801 918631 642767 718996 300983 586742 660741 940966 728631 878243 561157 585359 172561 894055 574787 221078 964424 287955 650404 240437 461968 135441 583984 183074 700099 792769 972768 475338 733165 923559 457816 006043 573396 113015 279567 482187 796784 966126 870071 367682 716387 043663 001153 087813 428502 860914 741891 495011 087099 554007 756235 187336 684358 018280 574740 240870 589378 867528 850356 029533 391309 376197 880815 112332 500185 355021 094269 058209 781194 640145 380001 / 47 > 491149 [i]
- extracting embedded OOA [i] would yield OA(491149, 1151, S49, 1127), but