Best Known (86, 86+∞, s)-Nets in Base 5
(86, 86+∞, 82)-Net over F5 — Constructive and digital
Digital (86, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(86, 86+∞, 150)-Net over F5 — Digital
Digital (86, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(86, 86+∞, 362)-Net in Base 5 — Upper bound on s
There is no (86, m, 363)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (86, 1447, 363)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51447, 363, S5, 4, 1361), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 808922 337244 520390 956787 096394 248147 459660 490401 998362 972584 082700 647146 050915 856897 844800 207925 238610 025101 426365 269147 478343 326969 920243 994205 172028 329041 610616 300908 973694 166768 215430 193502 149152 931460 872122 705404 262016 927311 824189 365060 176120 728615 132674 756626 890398 105681 425559 052658 940044 854181 148967 288565 857366 251755 141941 008987 199502 428869 948491 267913 227908 405592 467707 773007 041433 583451 496881 974079 561943 922115 650690 762423 939958 769640 335110 366663 591317 470985 114048 454329 689097 702337 037873 666612 727388 100130 398535 229086 000871 320424 497877 329465 898808 307956 886186 266657 436396 790626 197908 130627 474551 341261 646322 365886 233033 990899 940131 558009 569155 231417 743059 295717 143458 469535 123696 426496 298276 578339 789374 611115 866896 749181 524419 019279 905108 118293 006560 793011 090885 794817 091675 495476 461961 005784 192236 413944 035603 156218 431003 613593 147139 167802 810752 373028 457459 591000 548564 578328 211763 627205 117308 984755 198735 355345 354290 709070 618347 723809 575169 272365 716767 163464 594181 387923 299553 222022 950649 261474 609375 / 227 > 51447 [i]
- extracting embedded OOA [i] would yield OOA(51447, 363, S5, 4, 1361), but