Best Known (180, ∞, s)-Nets in Base 4
(180, ∞, 200)-Net over F4 — Constructive and digital
Digital (180, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (180, 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
(180, ∞, 215)-Net over F4 — Digital
Digital (180, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (180, 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
(180, ∞, 557)-Net in Base 4 — Upper bound on s
There is no (180, m, 558)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (180, 2784, 558)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42784, 558, S4, 5, 2604), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 457424 968671 975874 169334 922543 350008 703489 803131 466296 915310 585747 346573 987267 659637 401703 605169 665065 310299 804143 632168 544858 718033 316108 582493 926708 622859 905791 678817 444588 628313 096722 642615 366134 061006 672967 085399 484777 480837 778945 273758 314325 638814 133199 969638 966828 319428 580485 624119 746673 097784 310928 358033 420152 237964 037404 391219 263055 241070 843925 944694 521083 378638 051136 842860 182649 093093 862625 149604 356491 711273 743807 151495 811872 726987 698642 078328 713867 663080 351365 028769 734280 646998 716938 682044 022686 838246 528196 087826 204180 486357 070682 173040 839346 079964 609665 182963 644405 944212 677728 108040 991640 955510 631255 781811 970877 566344 773803 566807 361082 130992 474932 807159 522178 657735 888967 010715 567862 207133 734973 510410 644868 387052 375190 125133 398129 936165 135823 094908 062868 085998 848732 383479 264382 657429 424047 129794 323176 722221 966627 514122 173448 797539 325450 750179 332347 987780 235552 664473 695904 837566 666505 357012 802035 020469 134179 904033 581740 709573 236882 321460 910107 544311 847060 025442 915751 077522 444703 684546 072470 495185 561580 293421 085380 622306 972343 697500 317512 997422 777251 752273 168784 454034 718602 824972 403236 092928 932364 954873 146038 316669 310656 494189 320381 248519 925193 562858 270712 707075 029289 493237 197180 809266 282261 439977 415085 824961 710177 530923 513405 435719 939686 191219 759988 877181 945439 409123 057197 713701 798279 378884 302746 873084 426091 371383 733190 703898 936746 472887 118303 148612 767578 010148 208113 782530 727587 458875 324237 893314 270064 077678 430366 441120 719204 408511 720698 598087 943141 255229 260678 929069 184118 610860 541355 970660 844567 574355 911159 421185 479953 590683 304371 325855 376216 517642 896942 293791 391847 545354 732707 388317 229025 416075 179748 420081 186924 538183 348768 420102 908319 629312 / 2605 > 42784 [i]
- extracting embedded OOA [i] would yield OOA(42784, 558, S4, 5, 2604), but