Best Known (29, ∞, s)-Nets in Base 49
(29, ∞, 344)-Net over F49 — Constructive and digital
Digital (29, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 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
(29, ∞, 1489)-Net in Base 49 — Upper bound on s
There is no (29, m, 1490)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (29, 2977, 1490)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492977, 1490, S49, 2, 2948), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 829806 779435 137308 197339 302115 480334 451185 349847 706559 698611 677513 400600 670142 095611 018352 359464 939815 351354 524635 992794 345951 022623 242220 924106 224779 820118 168512 473647 397353 480460 067878 940397 419849 209965 978304 226193 478621 336014 991309 191635 030219 743734 877294 242839 889289 636616 125486 190466 340050 378071 114672 253619 116379 819229 852477 000177 891020 680072 283068 985803 573166 918565 311109 287941 235122 002858 804786 939178 868330 107566 672456 121302 307829 545185 540003 063085 000727 893490 926951 521215 962463 889071 859911 215761 075859 094242 389518 192139 023651 079958 793945 504773 244453 946235 318422 969080 674811 403938 134380 430505 543772 434173 363457 502822 427161 047276 864552 358847 042807 752883 997412 014874 053789 706398 918625 947912 504110 870646 276425 452466 733089 551019 247810 462380 064030 671028 418920 237445 453121 445179 124328 037090 181814 378514 115165 303828 536408 657328 975990 816020 665958 949729 388319 687134 940464 607430 643430 751300 641410 432205 508493 622153 586271 394234 011557 371258 731360 232784 950690 325453 379911 186302 867107 559505 769565 408155 892831 664150 062288 602235 902195 954372 128787 330951 206576 545901 390999 902100 164530 189867 292195 771370 332943 663319 906118 513540 802115 616631 682894 241422 817932 164957 742336 031501 405127 333392 370896 662429 060790 045701 358317 994737 430196 230758 505756 418476 507322 243267 233843 311726 677438 373617 894798 559728 260834 630280 510065 683004 317945 061881 171658 029540 910560 750581 467937 849235 694714 411460 622899 097339 902557 950287 180810 210948 401084 741535 171259 514938 816765 145824 742853 452902 037093 369912 991571 212170 070011 298465 470469 139912 391733 515994 009762 441511 555211 841074 431414 706909 933611 485261 998059 108180 494578 617615 205234 058415 388899 982540 869671 782013 190924 293866 413767 560449 778990 021825 813429 931834 229603 672660 594815 202999 256700 101705 382373 980128 957035 482804 338268 633661 820097 233202 417152 236499 215355 793038 061508 610220 110740 615765 432081 635872 531213 270017 710739 151251 236661 575800 311561 783972 868029 535911 955384 085740 814292 092609 645450 207835 797194 503549 173555 855131 990820 781870 416933 628969 398289 574810 238439 318101 624987 231922 538216 272831 454792 388808 911926 147195 099857 582505 409930 081950 052032 319450 409757 793215 851682 580214 746731 632131 028455 926544 414996 022547 568536 166401 393687 896713 113368 972606 436884 895490 787000 645103 007832 552902 120653 053575 483734 359760 488936 662512 168148 396875 220337 890993 662568 080881 913598 292427 807243 413653 210611 326438 453664 881134 603552 931630 236545 972424 406004 302616 252976 888951 602491 786087 291742 174696 041455 316554 177869 229084 248131 459256 006831 599605 302431 486356 073536 765868 286362 241696 357888 704144 760726 577075 199333 271532 680647 409311 821620 853316 074700 071985 206765 303158 257580 602641 552413 430439 507548 951708 210010 041860 577142 656322 835610 803888 229119 527454 448891 573825 351406 799555 710111 892930 778841 671574 335871 171681 270282 764716 036139 617873 962082 444395 497579 330281 208421 818508 852907 200131 212226 273401 649511 861999 797338 384874 821619 950769 198021 051242 004537 514125 555210 228761 689810 474021 583979 831605 738577 952348 392421 390827 622802 346755 574267 352446 026428 665107 313900 100604 984973 897246 712645 179751 042405 793075 880238 696628 409146 898979 171942 682514 958467 002614 150304 568341 804368 910540 003859 631239 014938 067685 709662 383737 180345 973871 308827 198202 367091 100337 332960 715726 674024 679553 105144 637823 791276 111798 046536 269022 089277 922413 064447 545365 409458 858052 060195 518810 683158 046703 305008 589498 983358 674919 121882 846497 062892 617379 783462 424681 108793 345649 934348 112214 872666 305411 139092 474404 401610 423888 588702 036013 717955 188532 369486 703204 454206 188275 080849 276116 619687 550225 619457 215147 950674 628508 623957 299039 684263 263430 080948 669821 663139 277839 344751 437911 799009 669329 424217 184751 684733 059087 909410 653164 776038 818522 758658 155365 493852 328371 946607 411072 658426 982541 011761 803395 053649 851273 251366 222642 171437 870804 293734 351255 041267 401982 605464 934982 269230 820033 037187 157036 194312 417446 578841 212038 555216 639741 545900 208933 526916 459556 766109 536726 601252 467365 767254 982325 096822 412994 857169 110795 975111 673363 489956 459255 218338 232087 709325 248493 651866 487886 756440 616688 662232 551926 089781 165365 897252 409778 758052 655805 448623 540349 097647 031359 870971 835144 281715 122996 206846 640720 460252 328541 421401 003342 822848 710820 034372 674587 670792 605010 330662 483000 529081 668311 177131 839631 475152 140761 365878 343097 315704 465337 047970 225659 544939 065480 967951 830067 859204 995399 322280 478573 550254 794470 322770 452005 680130 638677 456421 213983 050409 369273 529099 975187 182562 811225 699879 529045 266606 886583 766079 017899 660909 310545 038019 935676 382167 797963 088736 813724 297332 589918 590283 374503 637151 508189 807046 331329 907970 569813 343936 630699 984648 755683 338263 327168 606354 790648 459700 521030 759129 435486 478587 376219 075038 599953 458909 062193 096285 596169 127455 486713 504369 341316 549056 498916 223127 466850 150459 461453 022712 975611 172420 158999 845644 092451 347563 800620 914971 606008 655376 869045 803472 599729 992105 443610 845169 695758 059811 719416 652974 194229 675047 272685 491834 675284 563560 575553 992434 994769 000950 312387 462768 176421 995299 137524 661258 274280 082209 434487 661619 350071 650440 901237 508208 834094 473293 241524 671969 179916 319206 455846 799123 664910 314145 279151 879324 660179 468148 868357 765012 708508 446480 482073 872823 / 983 > 492977 [i]
- extracting embedded OOA [i] would yield OOA(492977, 1490, S49, 2, 2948), but