Best Known (176, 176+∞, s)-Nets in Base 4
(176, 176+∞, 200)-Net over F4 — Constructive and digital
Digital (176, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (176, 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
(176, 176+∞, 215)-Net over F4 — Digital
Digital (176, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (176, 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
(176, 176+∞, 545)-Net in Base 4 — Upper bound on s
There is no (176, m, 546)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (176, 2724, 546)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42724, 546, S4, 5, 2548), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 345770 915800 540183 673292 920370 244126 124059 694235 005195 217862 909438 244651 972649 432764 118018 641790 079570 419057 409600 747917 682901 058139 763977 942578 346174 710071 897796 939702 263844 215823 398266 269264 732223 466315 147768 333111 667985 236939 636073 590964 440615 103105 858249 079022 217001 729958 293120 332599 674128 918858 347499 773149 781548 033829 885380 747271 424015 296968 175810 863615 049381 118891 372223 969028 747991 380709 368717 266656 759905 662428 238661 243101 716299 941275 311356 172790 318363 364690 779297 589673 116622 736605 229019 794156 369201 450852 671667 070843 030540 941924 113843 155373 813409 504913 785937 549674 338902 606788 009281 906126 582629 104204 331454 300926 083200 682165 320710 563184 577376 362174 667589 276642 091268 310057 726905 266103 858321 444666 020978 184137 330693 011226 591801 607671 278080 664166 206554 315070 908810 184324 015147 071338 685040 517656 546354 505835 909300 870611 262676 488306 997224 151697 491955 539670 069130 625423 108027 975192 596695 627476 374810 906879 634287 653765 291933 892313 135313 647122 678619 867257 776219 237267 499109 728023 255333 701829 475175 975723 247707 033949 610533 125494 258118 706507 567158 079713 602002 827363 688665 123333 890966 772631 450094 915861 586702 054265 162549 960964 835306 467742 835038 810724 122295 415683 709440 507214 926098 099093 395160 631824 369324 663876 225808 493337 094582 362313 915576 127345 446759 650579 345339 269024 421320 556665 674533 562469 909196 516532 128338 238907 945491 458828 252276 595714 921123 643347 509355 342423 954131 446893 632111 242585 214297 406726 411933 784607 703211 093024 554762 178129 879634 405970 833768 060214 271358 018153 842021 318189 741910 075101 147528 840883 749301 741087 377810 926204 692676 097595 609536 441702 930569 684649 751408 700088 422046 279261 939748 065765 877687 217231 033701 300614 503132 561408 / 2549 > 42724 [i]
- extracting embedded OOA [i] would yield OOA(42724, 546, S4, 5, 2548), but