Best Known (14, 14+86, s)-Nets in Base 27
(14, 14+86, 96)-Net over F27 — Constructive and digital
Digital (14, 100, 96)-net over F27, using
- t-expansion [i] based on digital (11, 100, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(14, 14+86, 136)-Net over F27 — Digital
Digital (14, 100, 136)-net over F27, using
- t-expansion [i] based on digital (13, 100, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
(14, 14+86, 1358)-Net over F27 — Upper bound on s (digital)
There is no digital (14, 100, 1359)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(27100, 1359, F27, 86) (dual of [1359, 1259, 87]-code), but
- the Johnson bound shows that N ≤ 120 565855 555823 994593 558353 327127 670158 268207 095428 818203 174235 135732 789140 501134 460211 349334 802922 719867 209435 303886 971987 029572 297740 116834 166581 349992 552986 707777 918356 468408 453137 162550 128892 660432 863298 174876 804435 313856 492944 693868 175276 226718 488575 651221 394471 961560 362109 516128 118339 537095 151291 613399 945235 551953 620871 586294 265757 850296 362251 483744 652283 384252 006393 335987 638154 183531 039958 178789 010885 087020 358130 389209 195450 262431 788774 849837 529489 099953 853736 832906 746807 430458 923035 997198 273720 512661 459881 835131 252732 090906 858651 184227 786547 322465 553630 151354 659360 255475 613181 765012 197164 809276 386734 612232 714998 017791 855761 751737 744492 385167 567208 831630 502010 281887 005049 956812 654960 378073 248650 199899 177517 669853 456388 557223 430907 631514 010523 324996 969589 709349 170026 897594 254484 599247 091066 975630 243953 592077 956173 710951 969943 258219 042838 567697 341196 408719 639896 923710 216393 108787 839295 590205 828800 903414 630973 801696 931837 976925 640020 977139 727384 385891 107962 303638 220396 969143 574000 482051 314182 546963 293617 828565 526603 053282 798344 270446 012896 634535 607373 915293 432163 105178 093291 787588 334503 975992 625330 633906 441229 391555 080944 468320 134860 715916 490052 833923 821056 986124 903313 234742 753867 432986 444174 904653 268657 129231 687845 828825 630468 955915 826059 325899 728533 412914 820994 681138 730837 155781 833237 656471 975172 339215 681595 092112 663464 421662 758774 024100 459221 710431 194919 882556 343781 695608 862361 046869 913381 925919 573679 795574 857492 565954 738023 074740 718309 253895 808743 095413 217840 776479 378743 173033 044078 149285 822512 259793 600638 989695 431680 987616 931455 499112 059882 114613 618181 446478 321844 316935 741940 884107 988431 935353 290146 317087 947997 986298 233586 989122 255289 903407 952898 462199 813236 484694 260856 007267 768535 284520 837721 423343 715345 406714 922807 122178 348376 606952 422854 391022 463049 275068 531015 < 271259 [i]
(14, 14+86, 1361)-Net in Base 27 — Upper bound on s
There is no (14, 100, 1362)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 137810 364002 318038 824498 548384 294002 198596 667232 579326 539956 786550 678377 498939 089260 186119 161368 086181 329890 979499 080823 154197 057420 113068 645425 > 27100 [i]