Best Known (28, 28+∞, s)-Nets in Base 32
(28, 28+∞, 120)-Net over F32 — Constructive and digital
Digital (28, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
(28, 28+∞, 257)-Net over F32 — Digital
Digital (28, m, 257)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
(28, 28+∞, 932)-Net in Base 32 — Upper bound on s
There is no (28, m, 933)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (28, 1863, 933)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(321863, 933, S32, 2, 1835), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22867 960479 549101 919521 482406 611787 157039 221203 269032 252536 335489 297364 159812 863284 005564 383294 626191 188798 780083 862468 241315 194428 704631 141763 693205 200856 764002 995441 901657 368541 356097 141706 692592 191154 306993 838965 348322 896746 787971 848702 219897 963045 455949 477104 320948 277338 443199 748246 671581 232736 062791 480269 740903 849762 805954 411088 289856 618230 850586 356342 028233 072613 500636 429937 256256 217018 017574 118150 636472 963146 287066 225676 659404 204698 410404 556902 371984 582658 137425 442567 226259 935256 316433 811462 738966 866153 628992 362751 613273 531289 839505 712115 841363 697446 001435 952417 451704 005507 724276 290024 528058 458484 882734 610728 742814 337992 442779 188369 215540 761724 323289 267963 561222 733875 323085 355274 994063 026275 295077 642506 857250 178629 423997 242049 631365 924072 789974 090559 905579 832335 572501 265433 558583 297030 246528 171929 846850 554194 322405 379972 128581 171144 241854 664182 411598 377848 114321 931503 981778 806587 255226 167211 503555 638164 087693 143023 811723 869263 398947 980031 052783 758636 102392 322670 287669 698592 046706 013819 972359 945612 752389 799511 484216 232103 471079 711163 304975 523573 227152 468438 850462 279322 798415 229732 824420 208155 885101 620759 177323 197133 874200 374646 840866 314675 483038 969049 714586 714772 214462 950985 846606 876997 853695 703312 924663 845454 279218 779414 116050 754848 417707 654809 543586 026226 507616 594857 723290 592675 662851 936601 846536 880183 718489 680695 661054 191883 367063 209371 077152 887689 004402 290168 905889 169966 647943 716050 286931 121672 090148 699621 789325 679428 702877 874001 646461 304175 912712 396481 350125 363799 241084 267716 174147 497415 192946 582745 846598 954009 407904 064289 574914 417908 240116 795454 596563 276979 829264 459611 922826 024903 329029 903786 256701 510316 893030 400352 706414 959271 125007 283057 498060 548220 754708 778142 162895 973237 579503 562782 402198 362236 797831 832930 306568 390134 506839 890438 728863 102210 909222 274371 216540 884999 088216 284962 256313 051748 026676 721988 516482 807176 162846 722668 984988 930722 449007 124053 954161 507955 714165 392867 228290 734292 832306 125692 671491 806196 267896 105326 308275 864509 428692 500098 552687 665396 288100 581299 382626 908748 454854 549654 716368 326992 087045 630404 292514 543451 348879 624604 608003 909107 223923 819082 346637 209091 130858 805395 458469 032705 974917 869710 408599 701976 291442 439435 785846 009863 316821 677388 902726 574688 554218 197842 491691 820123 647534 290015 918265 457453 843322 427089 649963 027373 390581 560848 514003 233884 095294 850711 046405 657862 600251 406798 968080 660095 637779 699749 256827 692950 040549 256174 318678 743551 514315 028321 871131 333522 257971 466707 969317 217475 540726 909965 604732 302368 959504 498749 867037 614568 254071 925343 340243 766697 714005 071715 103009 321065 440786 167085 133419 346749 224609 557459 329382 397270 235028 123627 780269 232101 857458 129560 123603 617007 072833 866547 750583 987009 459265 218750 986137 642517 499326 040635 683131 003217 550290 559444 382716 868375 419082 725868 186665 690489 205862 807231 095760 644141 707335 565312 / 153 > 321863 [i]
- extracting embedded OOA [i] would yield OOA(321863, 933, S32, 2, 1835), but