Best Known (185, ∞, s)-Nets in Base 4
(185, ∞, 200)-Net over F4 — Constructive and digital
Digital (185, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (185, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(185, ∞, 220)-Net over F4 — Digital
Digital (185, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (185, 219)-sequence over F4, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(185, ∞, 572)-Net in Base 4 — Upper bound on s
There is no (185, m, 573)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (185, 2859, 573)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42859, 573, S4, 5, 2674), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 648 963392 631985 161640 252694 614345 287364 989834 374300 889822 894203 485816 799240 991712 780700 883190 529904 564434 350652 970666 300538 671625 120798 776718 128728 130005 519677 453514 893706 167228 046852 147933 336182 467689 850444 597691 045141 031694 868912 035358 450535 020468 501884 451695 392084 720372 928686 328448 598455 921758 061855 418021 274746 264174 572918 685013 625226 375043 501637 785403 466088 052203 780260 549534 848927 560527 457903 797622 615235 599919 143147 997765 024044 991636 486069 252384 174474 760282 377883 247006 794889 044055 764875 016394 179774 655620 448011 387303 374934 656157 956543 324965 369357 424415 870619 619452 379073 007155 009879 641225 114390 771745 046945 011802 401220 634632 669862 362454 491020 133814 468522 077674 898243 318643 760600 253978 064204 597058 940126 936959 808422 573063 653653 766169 175246 395339 369293 393723 223452 723666 696640 559047 006043 543851 383228 060775 034383 411470 867236 811903 124765 900739 350014 985636 483960 951112 631542 129358 760552 886096 110698 096533 740958 316513 108849 996905 764670 108294 498955 311765 712809 962148 782665 893763 997100 206575 843550 429192 718067 084521 956743 532858 198666 916196 924170 381362 122995 116065 654571 563258 814113 299032 161421 277448 816523 866186 977874 177263 922161 322797 618547 729637 360701 280294 387393 828723 659781 670937 564265 198742 973518 742578 670161 033933 097786 016128 419228 910214 416840 462830 672920 351702 485288 360328 369227 011028 303237 135549 552510 790611 981493 158802 863852 189398 775394 363078 658765 746833 461126 459308 159476 806484 874564 408128 787630 182251 428390 473483 454383 211594 753065 300716 267274 423933 974133 395901 641174 300394 830144 473516 037912 973048 603480 823725 268167 492720 381475 775925 567966 191447 878443 990938 421806 035976 377150 722430 582964 672233 317182 505023 779176 355454 398027 205318 924142 560109 017746 114540 611210 341190 071936 362612 076917 934921 956998 631028 724814 839808 / 2675 > 42859 [i]
- extracting embedded OOA [i] would yield OOA(42859, 573, S4, 5, 2674), but