Best Known (15, ∞, s)-Nets in Base 49
(15, ∞, 65)-Net over F49 — Constructive and digital
Digital (15, m, 65)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (15, 64)-sequence over F49, using
(15, ∞, 92)-Net over F49 — Digital
Digital (15, m, 92)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (15, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
(15, ∞, 800)-Net in Base 49 — Upper bound on s
There is no (15, m, 801)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (15, 799, 801)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49799, 801, S49, 784), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2439 568090 664027 470354 233268 237377 850823 416875 273711 654684 896832 972405 554974 887084 475237 356484 820427 937600 410189 952692 278521 312097 442740 514774 505454 610758 917919 454995 758643 047217 866732 825442 186051 802232 398221 484572 917497 862330 362356 518963 248530 677573 862756 009428 330783 743943 086306 846053 998669 468390 770122 592961 781791 992954 822976 770359 178192 566881 236171 923404 381442 117196 993386 244772 009029 866385 805767 234138 309980 140006 439759 413242 024894 410308 308315 580196 858446 447067 919784 258104 281895 107911 369131 288938 442994 814024 225872 612220 131344 308983 808777 588693 121799 880406 584485 222036 983718 724033 985477 579844 716087 813741 935788 265918 803882 360029 500845 121487 532397 741479 476092 045473 396812 588846 980630 679754 699541 299743 622236 393323 281578 304006 551594 637057 813488 836098 410933 759056 036702 638402 399407 040704 799415 635027 998096 864577 624915 161689 430855 183792 877212 657574 438643 510773 836169 467892 653259 323357 475624 823159 433989 649871 950190 573765 979737 688106 544064 387741 968284 126337 106481 867723 412103 013655 520644 402746 378374 591029 512302 325103 965043 974951 123643 345818 828846 744302 638008 821447 262918 605016 240556 302593 279739 647751 843729 793393 409447 395957 389977 435379 064748 174224 195833 418930 330028 209590 222204 138488 863561 174271 762272 734605 846353 362915 570164 872013 885591 273217 744443 762652 282156 770967 022392 027136 780407 165255 819879 147687 158269 077366 212933 605833 812660 756682 988432 320017 / 785 > 49799 [i]
- extracting embedded OOA [i] would yield OA(49799, 801, S49, 784), but