Best Known (25, ∞, s)-Nets in Base 49
(25, ∞, 344)-Net over F49 — Constructive and digital
Digital (25, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (25, 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
(25, ∞, 1297)-Net in Base 49 — Upper bound on s
There is no (25, m, 1298)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (25, 2593, 1298)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492593, 1298, S49, 2, 2568), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 243700 496545 375441 315301 559060 165322 029609 005305 088849 914617 813269 365922 353508 185998 016055 309099 768662 956238 934231 866501 025527 384278 773514 066756 233131 857338 400980 264538 564065 744636 656568 757512 646894 947211 411624 393697 737448 477771 384224 608041 723938 478388 528032 549100 809046 610763 639924 960136 960090 389495 505367 921452 458352 316044 898580 676688 467896 955485 848453 650170 649474 416564 100743 513900 342546 685446 839365 160645 127679 191338 617229 642274 710422 060308 854144 239964 440010 583082 121302 831942 196298 510176 468976 102054 767570 061202 264581 262397 730198 493099 310719 841134 761295 285738 183534 870430 742476 808475 754057 478834 584681 724560 890642 221671 774370 091324 435384 458288 809626 548746 813665 624833 368926 845916 625582 218798 809849 502405 778498 769399 642009 425294 922951 768552 201045 101125 316100 433503 807355 103269 209585 298439 662522 298938 682844 659123 646593 214560 569526 593111 834068 031787 937280 969029 370094 545246 740730 461735 217935 644378 539116 718973 223498 797346 457527 063627 951491 749804 196830 763360 960128 162630 113662 044517 248670 319758 490590 620286 380315 225180 206412 705396 734906 118188 214775 253350 986318 941006 003955 290068 966647 899013 463616 896072 282230 764947 955037 352181 263316 393218 079537 071084 995567 043832 440028 885648 404158 022862 987072 887396 079995 549760 221136 832820 631529 552161 793970 225411 284643 679615 623825 146740 045698 911884 031683 766548 388627 716028 534181 594375 850868 307886 533255 546341 763973 151604 013390 175964 274001 941470 194377 955396 363473 660986 684618 247962 271390 334290 356790 235943 702032 742143 073560 968675 390333 831352 966326 006725 221481 173076 317432 898361 933941 807494 078235 548955 708972 195614 951270 301402 856388 172858 102206 129007 362420 517778 571113 980736 697937 547359 010132 322173 620835 412446 506348 323588 817878 291297 897633 976477 039190 882266 861073 618924 791253 162161 258799 677539 805306 925771 710070 085142 844320 026524 069964 462719 767811 963749 293016 969975 921686 677795 018442 863754 627167 789536 652156 435436 805851 669209 935887 804960 230565 528824 288616 539697 168379 921623 754539 298307 875549 648505 930635 377622 732863 209743 632294 191603 269655 809773 494220 588799 373410 682523 584911 304554 287558 087472 717532 179008 483816 486528 754236 439931 701982 430746 430045 912870 846803 002020 835214 234568 168633 855454 523714 515862 505459 130675 736282 258130 774296 791118 760004 144793 107408 271540 341597 872829 059984 086499 951292 586658 303619 850743 677752 786749 616912 416704 326558 323637 021814 727935 086429 715300 822635 805721 638576 193790 559556 147422 087734 783751 748193 532724 442470 803569 858164 838756 989710 885652 864241 447645 761410 180924 706230 498029 362396 130368 643288 299003 122014 456530 247501 000823 679735 226098 101653 195540 350798 780687 260946 043743 585220 644265 234082 865187 210559 434703 999470 839865 161933 270014 500333 310182 288547 146600 701318 147574 301207 376167 261204 732520 795135 110968 355133 761938 572551 206748 956053 666616 538259 607074 510406 569594 168026 684495 929445 222622 899574 448974 872618 114222 563042 600610 697115 211677 881808 830259 178230 418863 619573 299366 190600 505200 952195 122064 837393 007100 906463 015875 494389 407971 520479 107418 925009 259866 559645 994863 813406 768981 213544 825219 462919 552601 555784 323125 256301 947205 305247 435821 504126 721175 939014 472401 683243 209120 326993 091733 867985 785651 168434 153212 712984 501608 160160 044519 078936 201278 085760 750354 164624 678950 549806 521647 137636 649591 387863 425065 140462 913050 769349 329179 962693 987968 947723 707530 285814 121139 727942 256630 472193 058324 355603 062720 780691 944390 002414 207523 866168 598376 368959 862721 016428 562056 715851 301149 229544 026345 263616 792504 721987 635698 501037 605999 098649 157998 932472 160089 613491 211500 929574 571925 925109 306786 365087 596266 827929 310543 126473 241100 995834 205511 906387 626642 531957 700846 472379 149620 366777 979671 131587 143103 538212 939478 036922 131367 796578 198568 231387 334425 090057 209638 197234 814311 269614 565864 137804 438428 017536 141700 573948 907582 754189 910864 499290 389937 245064 682182 845901 683501 658698 000755 676206 584993 941935 712980 535672 027937 205931 422406 833744 437963 179848 799290 544634 300177 171687 504613 253110 125836 214702 790327 031390 798173 656189 981859 031729 083093 833994 411911 267626 398999 458365 974531 474529 222442 117659 771153 441468 127787 878470 599938 149975 053933 786382 328890 529242 316513 331802 565942 248979 971573 377132 557820 019751 916029 315633 353983 274359 499605 112080 535276 008319 569962 668381 550042 627698 558042 302294 819674 994311 668013 252032 640505 215067 658173 255222 709800 768816 586226 599589 368218 020291 946121 614326 259706 109849 292987 768436 273893 687559 100363 931153 200865 555092 283550 294428 094206 772156 591488 056553 485899 768512 719092 079087 835333 889799 878904 820004 415263 730639 / 367 > 492593 [i]
- extracting embedded OOA [i] would yield OOA(492593, 1298, S49, 2, 2568), but