Best Known (195, 195+∞, s)-Nets in Base 3
(195, 195+∞, 112)-Net over F3 — Constructive and digital
Digital (195, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (195, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(195, 195+∞, 163)-Net over F3 — Digital
Digital (195, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (195, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(195, 195+∞, 404)-Net in Base 3 — Upper bound on s
There is no (195, m, 405)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (195, 2423, 405)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32423, 405, S3, 6, 2228), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 343747 006709 023122 518031 817899 821766 309528 246722 921120 871410 199364 523618 116396 629778 473904 683597 195902 201971 646311 537997 614024 172969 019429 748362 945740 786255 441159 427511 191189 798237 039836 387640 426114 582944 607857 694971 952365 559772 916419 480145 727615 005612 233110 296882 961529 651794 488330 350544 290244 034461 527840 604985 239423 673566 266970 545255 480270 741174 242967 851602 289387 040204 144300 036696 884146 659499 108186 594558 161649 259152 538607 910505 373571 729328 370756 303354 099189 703343 341256 779729 709072 243073 063024 335016 303302 897879 735852 085463 329621 046293 853994 609862 475381 942455 151728 703638 347582 339438 512143 809381 811417 934843 659896 975431 203809 378880 458550 668178 072519 805430 868116 523254 585621 675256 973098 226209 154827 489883 768154 710613 385262 359955 127758 637007 991844 441822 862705 114815 418472 980249 632053 212630 312735 115630 395216 906135 959407 767569 726026 120813 808840 516414 276299 983228 269373 942266 497403 843579 630435 279240 972245 099022 225184 270181 292535 653752 264513 468307 239108 881200 002699 771164 264025 154123 018029 287735 934463 304713 973239 182936 928797 931693 484526 293175 505676 518170 551928 996604 934152 831108 255280 889720 936357 275881 856440 380278 281341 127848 235244 275936 178141 702924 830857 / 743 > 32423 [i]
- extracting embedded OOA [i] would yield OOA(32423, 405, S3, 6, 2228), but