Best Known (183, 183+∞, s)-Nets in Base 3
(183, 183+∞, 106)-Net over F3 — Constructive and digital
Digital (183, m, 106)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (183, 105)-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) ≥ 106 from GarcÃa–Stichtenoth tower as constant field extension [i]
(183, 183+∞, 163)-Net over F3 — Digital
Digital (183, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (183, 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
(183, 183+∞, 380)-Net in Base 3 — Upper bound on s
There is no (183, m, 381)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (183, 2279, 381)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32279, 381, S3, 6, 2096), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6885 032612 081129 975326 009711 561954 326280 099796 952009 202440 326575 063650 175067 201699 498615 768297 019988 766099 026062 649892 286190 920451 108779 352770 398366 377089 886042 359976 160326 569848 997781 262663 542867 151345 605828 485966 243856 401465 427100 784809 375317 350326 550220 662192 126452 447845 936159 764010 227860 781025 141536 316581 564321 576557 296101 306634 508588 206700 542208 631864 785089 698299 978739 873093 316513 570984 419223 302142 118478 281472 635344 885195 091928 467121 762846 955213 157364 206212 241031 201454 387683 451399 907787 927868 592974 390980 481640 689024 095692 342559 054407 880243 486857 287085 969525 977868 690410 259420 497134 384869 940135 095918 398399 661727 777103 621311 929445 782494 595927 396247 298114 244235 923026 968105 016055 880391 105569 518817 793157 845973 351197 758994 261895 810252 028850 820977 636771 555127 472619 194030 228472 995142 745580 762556 046466 530740 748053 084068 443572 174238 462187 107708 898465 036627 228364 358755 546973 009670 430871 431668 172727 440224 507863 456611 217208 018945 545529 168954 399930 421493 240532 206516 283926 101279 134712 646148 408905 963570 677150 183732 645538 460661 312526 907844 206324 293426 769530 772947 192457 189024 057448 553967 / 233 > 32279 [i]
- extracting embedded OOA [i] would yield OOA(32279, 381, S3, 6, 2096), but