Best Known (14, ∞, s)-Nets in Base 81
(14, ∞, 224)-Net over F81 — Constructive and digital
Digital (14, m, 224)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 223)-sequence over F81, using
- t-expansion [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- t-expansion [i] based on digital (13, 223)-sequence over F81, using
(14, ∞, 298)-Net over F81 — Digital
Digital (14, m, 298)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 297)-sequence over F81, using
- t-expansion [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- t-expansion [i] based on digital (12, 297)-sequence over F81, using
(14, ∞, 1230)-Net in Base 81 — Upper bound on s
There is no (14, m, 1231)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (14, 1229, 1231)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811229, 1231, S81, 1215), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 27 325821 101422 924912 433151 867742 552438 988902 892445 543585 809196 863514 243523 139539 651381 552088 713279 271816 362161 869432 071629 109001 205171 383864 326160 775427 081703 266259 098777 143066 207568 134004 193731 069877 637989 247777 101646 457566 640156 070182 542820 863537 947854 825582 437209 868470 261613 528489 772540 972711 052725 407297 498385 065030 539392 545083 973786 511868 603384 774212 207505 988105 612640 082251 483794 851214 080102 986135 619731 129087 155762 433192 078657 191817 254290 076747 976634 597352 138514 363009 389288 677130 653039 600584 902137 501394 158052 116870 665249 132827 364158 562921 759702 897526 858531 302644 482739 827424 122961 593888 526368 477174 236552 678579 353284 969896 223232 536752 381073 410846 919164 427928 093501 730620 016661 363057 344100 638716 963318 039035 791217 630033 259885 855936 089492 247203 860398 031485 542263 999957 505846 347179 102635 994930 026663 305755 615396 687201 047815 201294 544499 823049 282732 315826 049180 010381 934123 654076 961743 372134 409551 526458 240076 470287 174357 980094 148987 808141 872790 600670 246000 932654 430576 276410 563742 819758 467790 865293 182910 690336 368927 570596 429034 333735 871693 625702 664612 109078 726925 618132 333862 468205 020321 964075 192338 646932 227399 067684 164342 713306 173010 999798 817857 000828 288913 920592 963304 180540 867346 688699 003357 386975 158368 036870 210948 348154 900810 501921 613151 414353 179357 835839 848897 630427 182901 141477 766448 936779 438363 378987 116296 463664 438110 208036 110295 828514 086529 467762 381223 302802 207675 094276 419668 365115 957520 279327 692166 013483 251526 124303 079208 484310 738298 229901 192561 906254 655981 588055 746928 830630 197175 398051 410393 710020 797716 403379 670977 010506 744206 278050 564611 082430 124980 388106 793441 901073 455027 316302 438538 977337 387488 177029 319091 423598 182812 004732 216028 268340 342907 279736 419643 541959 873005 082545 529095 814179 502526 950020 200308 722828 707599 619124 499073 660684 486312 200281 531595 501166 894122 499290 946266 149941 942822 234907 186380 462101 893322 143612 618862 456217 814428 317154 241921 550635 619933 252405 404084 261654 107182 588856 461610 785804 138068 366130 534502 272007 135347 164083 848152 943302 784917 746831 960506 841529 307152 490397 179404 148750 363635 573056 027937 152043 571751 457358 112727 690061 889482 684137 733254 185335 424198 248839 068773 200070 249962 231414 952700 487537 403313 974227 911106 483875 434078 857505 269136 097007 011195 932406 984010 797359 705905 669932 571940 965158 488346 247625 332646 475861 707207 551399 136478 424237 991177 815040 039510 533115 776565 225203 956841 694217 718122 562401 / 76 > 811229 [i]
- extracting embedded OOA [i] would yield OA(811229, 1231, S81, 1215), but