Best Known (27, 27+∞, s)-Nets in Base 49
(27, 27+∞, 344)-Net over F49 — Constructive and digital
Digital (27, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (27, 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
(27, 27+∞, 1393)-Net in Base 49 — Upper bound on s
There is no (27, m, 1394)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (27, 2785, 1394)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492785, 1394, S49, 2, 2758), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 464334 893486 349881 135729 817308 286938 684706 500717 931362 936566 293718 650623 314677 051470 325213 001209 721434 506231 368721 290246 557402 047442 320325 714950 976240 433903 371082 180421 435509 905475 793879 503598 716848 461046 462865 391941 409360 915174 390172 729325 294830 785865 067663 872354 930129 381260 639919 204997 293724 646614 254663 339442 037992 188928 264628 868565 674916 825225 443812 088200 823353 847310 064276 235338 767497 971475 127101 557617 838913 667805 356460 326267 678674 770635 818023 018456 997127 505618 264383 136170 064020 828228 399973 192772 678917 278253 535674 314076 195496 139950 192922 535837 648026 085044 044408 450014 885591 702058 524171 667038 291520 798832 651346 305878 802069 737897 354683 761255 386972 229085 760101 836070 153002 958773 737174 175765 219949 867546 292117 718359 893900 448493 597293 344136 032391 173894 911136 986506 459035 803079 352675 104283 271899 223439 589678 344575 436531 928511 129694 950580 712632 726822 641924 891918 626409 145046 058364 186257 574839 057127 001546 620389 164456 224954 942707 400061 824720 482038 683567 369850 373592 553252 966287 067411 347228 871504 008983 041890 131822 109438 212622 601566 391877 733201 440709 072764 700319 903068 323921 338945 973291 802552 640349 134278 339532 994978 269573 190807 246409 661096 502417 755060 808367 688048 158214 276495 576323 014040 096492 513272 518071 702080 131156 177711 106153 755014 282804 562223 790224 956173 462263 954075 842305 762027 386682 955765 642784 459763 890139 460782 458007 411445 549963 426521 916797 059517 700729 530066 990769 790802 450184 468890 065490 108289 973247 332860 929028 520789 198172 689076 448075 371231 768310 583510 244405 670166 179787 647415 915566 839513 217521 868995 149231 182266 024520 875979 409740 733648 920883 050250 563079 250413 147776 088720 946044 397685 506706 652112 076197 246419 030538 108014 968967 288633 300327 041603 072459 977104 452079 806078 628766 707860 423960 396152 282060 663222 295617 730747 382105 508478 905840 158610 067036 189104 268839 418626 889164 545472 970617 677465 642615 153888 033132 503357 479836 234822 626734 794272 085878 400763 979889 391567 124441 806863 159905 710607 106015 677255 986525 600126 389977 729405 246766 464056 712942 110470 657261 059670 120386 651419 023349 625327 607391 568222 075415 093070 750714 420674 370527 523236 154523 069045 709561 838256 143227 956885 664837 615356 385408 230819 084654 210441 079333 238658 176058 974534 219457 843358 451025 141646 028824 629430 237435 892864 885392 843144 862716 521583 783243 323040 560219 444598 540814 760602 347266 159376 712075 258965 834266 741028 741472 025507 014030 356184 608874 214129 707236 538208 459505 231728 163949 793091 215076 282277 924382 105598 068571 951386 192515 673143 961493 123425 823186 414288 422750 367076 680764 355583 521793 110441 300261 513205 137032 688380 148209 156165 446711 080994 376714 991118 856108 139499 581724 081959 683517 482241 562335 958763 187741 971439 584707 759430 549424 593880 861094 447531 243104 543690 986389 003472 094461 496858 431782 214834 251489 598501 314378 970496 881472 693552 670017 164084 015774 681804 521330 393751 587163 745629 993820 888155 168198 556930 372828 622773 021164 557479 908770 223275 285429 372434 438860 595562 325258 780289 245975 672833 882890 580545 840835 829657 255185 614628 977541 821349 070945 122813 380422 466204 215524 051329 820519 301834 383566 013576 085456 362751 354787 049859 214581 531994 377147 822557 493214 198094 275924 790991 143035 234849 024766 908968 004588 634367 080465 759372 053121 582018 066079 476354 221190 030099 945588 312741 580964 413138 145533 396624 227580 622432 244209 356555 395507 116958 291354 213533 056809 725772 622551 664443 142109 836571 524053 384717 132349 738926 693114 393903 909478 550079 410838 077450 454968 439242 188889 192338 284430 348604 134772 669413 299134 115239 744188 233439 279862 251586 176517 649866 952666 679084 436196 344153 077236 926617 047579 970234 643457 415784 014483 428096 709450 608671 728695 954925 043597 946959 174884 636921 950885 352000 321437 934507 015428 832932 028246 158278 097196 195379 669402 231519 606064 964968 533060 648578 197975 420802 342861 826968 133753 335591 460809 901516 242103 056714 978755 517958 416224 826527 285406 226159 156215 821380 850851 481897 569840 947499 647580 884843 074508 022395 382434 775289 547931 831848 194391 215971 884311 362921 056540 887859 093625 052426 994850 951415 415020 938615 554038 206389 503390 958478 924723 937318 520903 207038 921029 027670 329956 881687 329729 343024 295448 707626 481083 289217 304628 917831 728757 086208 010449 659589 559022 935090 153182 533895 047150 896475 014013 499504 866418 052844 487967 737400 747631 116271 606490 356199 790874 681767 669870 507838 434654 728211 686506 979852 614722 977151 931839 670089 728414 293274 545778 687579 092987 102517 862809 731235 083112 318624 939192 811987 676980 576422 508790 228877 637558 854499 081098 301472 301257 733387 118543 152555 117748 525627 621240 599846 162977 490954 097687 947070 514935 145182 052834 139541 274855 205809 557393 473742 214075 516842 160059 762501 991046 267479 960259 557804 380743 593466 019084 744805 040650 665678 140255 392771 973333 331039 926080 228413 654902 768272 329515 246593 350601 888164 891728 489234 879148 319220 015896 212350 619067 097233 484179 110990 703198 101493 598273 636147 849605 716091 138359 288654 853348 406576 232537 949672 247271 / 2759 > 492785 [i]
- extracting embedded OOA [i] would yield OOA(492785, 1394, S49, 2, 2758), but