Best Known (152, 152+∞, s)-Nets in Base 4
(152, 152+∞, 130)-Net over F4 — Constructive and digital
Digital (152, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (152, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(152, 152+∞, 215)-Net over F4 — Digital
Digital (152, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (152, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(152, 152+∞, 473)-Net in Base 4 — Upper bound on s
There is no (152, m, 474)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (152, 2364, 474)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42364, 474, S4, 5, 2212), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 64475 895487 968102 945094 202423 942079 255950 497853 127798 674109 659420 531224 291870 234479 624663 653512 573868 914092 567185 340804 973694 404758 374509 942555 736804 853325 215544 195072 919435 473032 675650 927299 925111 826681 143697 000498 460465 522839 991826 479221 814824 154619 678270 999166 738077 937388 678431 125162 278243 391978 930332 645891 158487 571236 122685 141300 558788 015375 869663 702719 494602 575452 321278 318683 739130 858927 592749 783796 278913 908047 802163 820222 226220 004589 778897 252625 507424 831185 825595 339506 980848 156709 031552 328925 674100 197554 545470 280357 126936 702728 123055 285107 481430 598962 613759 771144 490902 274871 854374 334670 524847 290020 601133 871645 495980 514001 687839 189411 424677 183365 809964 623603 795490 903536 911864 856591 122593 459655 961571 843134 729829 091098 197273 074481 016174 778699 772937 577374 010198 961000 150321 846696 761005 077169 954092 624657 396889 817399 890597 491539 840865 144757 404188 358624 785441 628846 142983 980783 351489 832779 303973 513210 375932 419247 201442 253832 493135 335393 930911 659453 055876 311123 600966 906631 847641 045814 220386 029618 689274 450391 295276 636734 761668 228941 403871 109084 559036 165642 429649 669945 897910 973699 690721 722318 540434 126173 692223 085249 551204 497293 891706 790755 831627 367662 570104 987087 357887 263512 037362 893253 590091 437825 319521 874594 066416 740838 195063 665922 417352 945781 182243 935720 553216 665031 977538 004490 901470 733382 384689 350208 580559 110621 838896 067028 910894 703366 611215 988471 793985 223490 452729 137679 953697 690097 604402 189489 715055 427584 / 2213 > 42364 [i]
- extracting embedded OOA [i] would yield OOA(42364, 474, S4, 5, 2212), but