Best Known (153, ∞, s)-Nets in Base 4
(153, ∞, 130)-Net over F4 — Constructive and digital
Digital (153, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (153, 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
(153, ∞, 215)-Net over F4 — Digital
Digital (153, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (153, 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
(153, ∞, 476)-Net in Base 4 — Upper bound on s
There is no (153, m, 477)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (153, 2379, 477)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42379, 477, S4, 5, 2226), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 69 150522 824331 256798 179810 576870 788539 031034 194023 765075 321528 289977 231575 509888 752151 032062 936913 669856 015905 682658 522430 579342 250613 621971 610197 725876 070867 244952 485254 276463 201746 985852 670162 507748 613931 156090 366099 491648 569950 818223 084095 912984 397011 013442 698649 408433 666494 145359 940474 769691 414300 387501 927158 898647 707447 719672 239101 804102 047410 834435 585796 384656 242380 149387 721233 953215 904450 469360 225293 502423 783806 349889 519020 087516 427012 348305 106739 582613 360290 757388 169547 365227 963973 753434 871209 696871 782963 006614 953477 729652 116238 038150 942017 647167 323894 845708 896108 103984 322235 512781 549708 033614 352856 038206 391023 644583 179358 904380 284721 126685 472061 168376 743762 231550 536199 774237 966937 173543 035756 513730 268666 953852 995028 908988 381898 440140 337257 874317 373059 904920 720477 395252 411354 138635 500201 021455 624552 327370 969535 137911 811407 048287 394238 934488 587046 088595 000475 894089 428023 917505 927837 973261 549307 776249 809339 154420 805505 689037 143871 168945 902369 822215 535766 137160 663161 526486 645267 559474 496835 301180 743396 157056 135133 561362 302343 629512 482556 746091 079354 838812 320705 588537 398132 195575 021827 268203 553108 845949 304512 614037 006887 515809 933187 455575 918721 183041 629647 610863 290950 175578 079103 300484 286836 163894 198464 544819 296482 807040 535529 490936 126389 912552 147574 611842 490204 597789 994508 472459 533597 925320 865913 049124 339212 558868 408443 907347 123620 691232 663408 770211 173474 251009 365951 303727 728799 125686 289864 244826 374133 514240 / 2227 > 42379 [i]
- extracting embedded OOA [i] would yield OOA(42379, 477, S4, 5, 2226), but