Best Known (28, 28+∞, s)-Nets in Base 25
(28, 28+∞, 200)-Net over F25 — Constructive and digital
Digital (28, m, 200)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 199)-sequence over F25, using
- t-expansion [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- t-expansion [i] based on digital (25, 199)-sequence over F25, using
(28, 28+∞, 723)-Net in Base 25 — Upper bound on s
There is no (28, m, 724)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (28, 1445, 724)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251445, 724, S25, 2, 1417), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 760099 920240 298516 053075 985664 782948 645576 632460 770777 670751 262364 259005 490198 431407 719150 888106 635649 856408 918567 460041 560814 369850 313868 059437 913102 442398 578187 289229 456660 381584 740736 340510 173150 594379 784181 934436 943414 677414 372028 045324 988760 130107 950447 947047 608382 553923 225071 542757 367181 855950 785761 292451 553355 685763 178995 660833 563076 729457 147892 142553 189432 909361 830350 327507 054543 229389 869547 668842 677570 356209 796240 109229 460592 432618 343808 552649 637970 158548 452444 192802 387556 275688 624080 156666 436300 303097 929938 287405 128411 690983 774057 622362 814086 889111 668848 427260 583326 886243 107823 082113 515227 890868 869793 989688 035432 593565 935731 850922 073823 428902 078181 517663 985263 734730 299203 203593 550266 151887 102028 783165 186351 762734 322392 963399 404962 592078 694101 776705 717319 009377 340682 856594 109554 508543 755692 575814 052927 462530 113379 976783 117933 823362 770268 921426 345953 915269 897584 417480 447690 254606 170721 267693 191597 011408 048292 811854 785357 532642 886082 346356 249581 554186 222642 750919 744826 083092 144374 370877 300743 417024 908685 507544 618339 702495 907388 944424 145648 632524 301717 583370 928035 369227 412998 394495 341633 779130 875797 864820 581893 278699 281517 881542 371533 537610 316559 897962 409114 043365 211839 960985 996373 499731 860993 264086 621496 484674 635610 989541 147405 820811 716409 397450 578986 969391 601806 850113 093096 471931 638285 592432 690377 592630 736789 217256 080402 879641 908304 534871 225887 770366 541676 141743 995548 081864 963256 463905 165455 886990 121632 127147 070810 141081 107672 306179 922027 966562 481478 403674 450748 583399 374309 460881 442260 903419 313366 128293 473991 015112 205125 105852 129604 105064 619208 056367 323490 594872 886061 530903 856397 498483 074524 290044 389649 673469 416720 199387 594848 623522 306948 117437 544649 997631 586856 371667 890832 920146 607468 269530 187884 784283 383251 700553 009634 748758 777174 741433 823747 267439 596279 901846 770360 040089 383060 127683 867662 110473 201899 374551 948835 965601 294910 443069 600045 958759 237202 631505 014741 548383 482098 791942 285772 853921 489312 664455 382997 245834 853192 937064 551633 300911 633039 920189 958138 507790 863513 946533 203125 / 709 > 251445 [i]
- extracting embedded OOA [i] would yield OOA(251445, 724, S25, 2, 1417), but