Best Known (23, ∞, s)-Nets in Base 49
(23, ∞, 344)-Net over F49 — Constructive and digital
Digital (23, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 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
(23, ∞, 1200)-Net in Base 49 — Upper bound on s
There is no (23, m, 1201)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (23, 1199, 1201)-net in base 49, but
- extracting embedded OOA [i] would yield OA(491199, 1201, S49, 1176), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 42 976994 706273 184517 836242 870443 598888 952919 639314 944049 734708 854494 166815 070434 187958 944604 113551 289453 446902 006236 685637 198497 885234 123426 214333 382369 107907 385983 980192 135992 064539 887169 131920 321445 501972 876232 775025 329690 349157 671147 096543 994066 000966 627737 916748 899720 315165 052213 942982 166823 081356 683217 013803 608003 652737 316745 995380 788052 844901 362884 583438 717323 675160 643217 738983 125422 647161 989107 266951 793115 706978 110339 270589 669614 307012 175149 414248 404830 244972 092830 566213 630306 218827 734350 098013 243775 820088 707099 969466 877870 106503 035365 594732 004751 683230 075060 797772 493777 977894 723445 484082 409212 649612 941419 836991 577832 777119 656904 184483 993878 584516 833081 583029 689541 058017 738812 753083 900398 132074 595425 977337 565944 635885 703949 538164 711211 745874 552373 442885 198912 357957 477975 968472 399902 558764 335229 975925 043749 092053 295183 041273 786306 653845 095596 884188 786783 425205 007974 600588 847337 472614 146218 711368 922698 653248 776515 540902 466235 612926 978934 570302 707341 614646 579299 946782 407716 664550 218735 432387 846669 787264 196168 815595 962505 920462 574458 272805 111750 757034 557426 697876 056710 368067 329347 076432 899717 404653 375964 142116 223196 256419 288617 141798 322508 183824 408901 597617 087595 385568 851115 796498 361321 979575 103449 878094 347942 798455 863921 421740 413567 600084 957422 438773 669919 347222 145142 621527 775597 793548 314872 090287 833189 342998 204031 672711 551380 930076 493352 737882 047736 238665 124541 319717 618673 160096 682537 343421 001742 364106 750531 035741 818526 137603 802295 936683 508174 049782 024511 360575 610005 674130 874190 304172 956965 475903 112840 649567 097088 632047 125680 784854 358768 872653 111012 915407 899821 694503 250910 501559 896498 192024 152464 447985 436989 148494 016132 026051 265580 229941 932460 178079 401527 509946 008976 936669 215191 025072 304217 014771 741484 405685 732368 456723 868837 470916 469063 665046 296605 121239 581610 646915 743796 263777 867741 316874 174275 081996 537285 836202 921470 790909 342087 200835 967288 736387 698294 859384 821608 911292 582490 933077 250692 708719 284148 773522 819012 511621 060878 667070 758901 451099 846507 283824 213204 836939 513527 191390 996836 000025 / 1177 > 491199 [i]
- extracting embedded OOA [i] would yield OA(491199, 1201, S49, 1176), but