Best Known (252, 252+∞, s)-Nets in Base 4
(252, 252+∞, 258)-Net over F4 — Constructive and digital
Digital (252, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (252, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(252, 252+∞, 301)-Net over F4 — Digital
Digital (252, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (252, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(252, 252+∞, 774)-Net in Base 4 — Upper bound on s
There is no (252, m, 775)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (252, 3869, 775)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43869, 775, S4, 5, 3617), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1922 738844 324427 888510 937483 945473 506371 023032 937633 986597 893712 796756 438413 361852 357284 556656 790887 043685 318576 106516 763124 587006 265745 326657 232750 719724 129017 718683 870059 618107 746976 557309 968279 579645 992641 430958 843649 566682 074864 552392 134486 129314 157511 315247 510632 348581 576887 815888 001840 451831 112485 499822 446678 801348 490935 119305 429668 749732 630464 678743 385311 292622 150958 471671 634648 578623 620732 627430 894457 145542 012982 214540 018765 557271 549991 096752 390373 020640 280905 806199 787806 182959 714409 619450 514763 093027 609992 358258 298803 095773 494600 179500 806718 537406 198715 638862 327351 878264 956186 348230 611919 043365 659796 026869 867457 576752 978780 827860 389845 736524 772190 121136 913067 035408 748753 898340 432599 425262 822649 278215 287948 209753 162133 053909 085618 157395 116743 721036 563011 639491 206557 118858 036892 652842 421759 303999 133012 545483 998097 418129 130713 348982 714299 215256 453860 235275 320784 593625 726755 615535 966338 100881 500811 401613 383826 108148 903976 747401 687419 946332 577603 470195 293007 977478 928106 102116 910744 228030 190345 447617 897716 292152 569854 412899 904802 066132 336403 783934 202955 766666 403496 329850 113048 955881 622373 502761 724953 696594 914269 116294 784370 005149 470036 631999 253757 596534 231794 908422 851470 088259 324010 828949 433502 816014 182844 707478 759792 026268 913929 556075 489857 338684 984324 649055 535166 919879 915536 836946 477499 577334 902504 888055 971888 878393 735571 539522 390764 298475 985337 691812 635930 922608 782668 427137 566348 160103 893873 027111 819014 953677 742813 088568 180880 148161 733513 886215 990978 359885 852784 493012 922007 762463 878052 998414 581388 590537 673673 724468 859429 962729 634270 529578 998720 849560 540180 342784 956226 889786 168281 379530 552373 919483 826387 417678 305916 214724 939963 190424 868845 545094 421752 608753 207062 276503 391609 087804 127511 944373 682633 478079 115997 877750 011956 552047 990888 652556 624011 554932 867886 931310 454278 856206 205598 861085 438902 029938 068909 625168 634273 995892 705902 512543 174805 645534 290428 893434 717312 227356 796154 039797 008963 892907 615193 320960 268728 157793 214229 422844 594671 233908 045130 139878 183224 930394 181621 600579 726863 835284 519050 766453 344667 895010 302867 874569 407612 003722 076449 306322 408251 841986 523353 171312 685408 134810 354256 245766 771386 447104 618131 352597 674448 240351 315132 369992 174358 382115 112655 364271 895532 327281 745391 547521 891153 496850 135674 299176 501222 018288 330914 425490 837377 345952 414004 762446 897910 093767 704909 690236 305408 / 67 > 43869 [i]
- extracting embedded OOA [i] would yield OOA(43869, 775, S4, 5, 3617), but