Best Known (232, ∞, s)-Nets in Base 4
(232, ∞, 258)-Net over F4 — Constructive and digital
Digital (232, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (232, 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
(232, ∞, 714)-Net in Base 4 — Upper bound on s
There is no (232, m, 715)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (232, 3569, 715)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43569, 715, S4, 5, 3337), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12736 877186 482647 401020 470015 637106 666674 205302 472527 912674 769555 395909 600070 621742 017094 940589 117068 266583 708393 495746 911806 925487 604563 954709 270296 758729 509456 636599 305563 011728 811963 556431 381734 669990 601339 801953 391661 745197 669101 898414 539007 833326 871363 799645 988053 243089 347731 340433 789137 234409 549165 444987 801945 037371 681080 254992 181608 998515 583351 435034 106560 699801 567557 628364 990900 931901 969504 767367 163668 729375 486040 117056 428809 102309 507106 916837 709962 345881 153871 621805 710196 430232 313480 426553 189058 287505 392589 432747 341396 378656 060505 726006 488167 887566 928733 863074 574799 253547 203805 387694 745263 513741 655500 724119 603098 098379 941505 415429 582209 568293 316424 354741 471357 065262 872471 314255 005464 071994 184323 819654 588316 639579 605555 454228 622565 584736 200727 652947 949714 078955 986014 825255 853760 645465 460275 799535 773412 238045 721185 296090 717853 896573 026976 356499 576354 605535 141651 506876 453265 179598 863235 601088 330680 481486 132110 721753 397297 158092 139164 398022 446495 173174 178202 654392 886380 278013 216993 929355 956153 599194 512886 837369 027551 563610 112114 248709 415281 432526 547384 616447 442360 406741 311203 420551 461307 955921 729190 803099 061245 948906 998733 277366 222216 533192 852128 500657 012904 923044 010919 127082 994346 328555 579469 565544 463327 858228 193252 339904 448553 145377 137960 457797 004574 214331 276530 051277 811938 202577 824806 834741 939240 192117 794709 899536 576705 071370 198383 025533 167770 968135 548432 859615 344252 796188 072854 561045 481353 232675 386933 061570 121514 847410 462480 102782 068900 234418 511805 112249 369761 992665 762993 285537 905592 845302 067436 357797 604564 518929 510324 975658 322339 589414 954598 939427 463167 955484 203235 548429 901110 857917 342627 075032 790647 322234 576770 930082 197330 073640 926508 067564 677408 493912 727075 340003 172021 861790 870223 322779 127482 815028 848688 582922 758598 229173 580117 476685 949693 294730 149567 760709 618971 505304 208143 772050 457721 106567 531699 057337 927264 048401 399298 923090 740413 025366 220639 289643 405076 852449 662935 436586 133853 396990 852829 078556 335160 323097 979264 278984 959639 059287 345716 975131 542762 530101 527416 188364 560694 640658 209669 448550 890539 003153 946352 747103 771574 619814 331334 964706 484577 206352 034908 980562 912201 020873 630972 290914 392279 496603 467776 / 1669 > 43569 [i]
- extracting embedded OOA [i] would yield OOA(43569, 715, S4, 5, 3337), but