Best Known (184, ∞, s)-Nets in Base 3
(184, ∞, 107)-Net over F3 — Constructive and digital
Digital (184, m, 107)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (184, 106)-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) ≥ 107 from GarcÃa–Stichtenoth tower as constant field extension [i]
(184, ∞, 163)-Net over F3 — Digital
Digital (184, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (184, 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
(184, ∞, 382)-Net in Base 3 — Upper bound on s
There is no (184, m, 383)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (184, 2291, 383)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32291, 383, S3, 6, 2107), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16447 214611 246350 654248 877380 054258 996708 897888 397804 297726 522334 043112 877298 051372 201092 843817 053221 251958 528856 166963 664278 876600 446077 053970 693971 559856 831732 577346 865810 672283 837289 092462 195920 989986 664202 330376 256051 645078 596090 875904 905632 962956 907355 093091 262682 866276 383690 018570 336909 207567 582641 368081 171055 198918 945695 839526 079022 524377 456075 140710 406814 325386 330129 652163 055828 583324 581682 452113 784286 215175 035471 210939 871898 504779 480427 435965 163842 047763 303520 505902 192838 286119 937169 640558 075346 432518 204878 084848 440052 301336 433437 313684 052990 842205 855982 880703 350131 332789 233983 407089 494691 923405 278471 682697 845394 035731 712889 350551 971361 801094 347718 271402 127003 868160 837788 970053 646713 672058 183849 831249 378112 793307 531170 896224 879975 019540 004931 999251 027858 543950 229346 636932 791929 281406 612277 299233 461554 368621 977328 090087 451412 095653 894124 551954 735235 896493 166718 966821 436716 157248 255024 737997 199935 966014 549200 617659 743727 907830 343780 337186 883202 618337 000875 079800 378423 601446 899166 825028 603356 998946 881619 267982 835624 912358 801496 227500 134261 971240 486746 462665 639391 832088 885491 / 1054 > 32291 [i]
- extracting embedded OOA [i] would yield OOA(32291, 383, S3, 6, 2107), but