Best Known (108−93, 108, s)-Nets in Base 27
(108−93, 108, 96)-Net over F27 — Constructive and digital
Digital (15, 108, 96)-net over F27, using
- t-expansion [i] based on digital (11, 108, 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
(108−93, 108, 136)-Net over F27 — Digital
Digital (15, 108, 136)-net over F27, using
- t-expansion [i] based on digital (13, 108, 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
(108−93, 108, 1450)-Net over F27 — Upper bound on s (digital)
There is no digital (15, 108, 1451)-net over F27, because
- 1 times m-reduction [i] would yield digital (15, 107, 1451)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27107, 1451, F27, 92) (dual of [1451, 1344, 93]-code), but
- the Johnson bound shows that N ≤ 5529 594681 977603 145350 071657 813949 387046 420027 971258 635312 921411 033160 978253 790319 145914 607449 002655 345128 533321 927798 419349 236513 650105 479584 669760 845945 392050 795468 372510 048188 589906 102761 083021 265509 251210 178089 065855 580030 422679 203268 000976 773753 976062 542340 106280 870146 473173 882593 664384 423314 501213 504282 085269 304889 738865 237167 019671 199285 442808 529926 283207 323613 464918 226780 933617 078567 645164 365919 822912 004332 386093 415489 664527 538773 036234 693176 343589 035854 099775 634829 372026 533765 931086 170520 259134 110245 100891 791897 807710 621511 705609 369143 259319 466094 071031 540622 072709 158302 148609 346586 098437 568085 701537 142786 593491 519681 426200 979045 060745 658608 250232 599805 573811 419590 392496 716221 289300 043112 299237 854621 445047 521012 703902 377681 763998 993739 982188 615754 512630 600452 478433 857457 521907 153858 275588 806217 780662 586194 982443 711530 300757 066333 951511 471187 668803 078607 522545 983667 331799 264105 324176 983814 769808 384951 223471 215290 424708 921296 729182 998440 301035 635054 829967 011761 322133 626355 148205 013200 789694 768194 791674 499638 950393 361446 532606 599259 561823 912477 206152 168464 698155 848014 206265 457639 309599 131689 538231 616968 902406 927596 703793 370204 515096 448717 224991 113804 054530 284893 324258 853958 791834 316423 525179 138765 472591 807516 017861 068576 494797 114735 225102 813125 508037 068888 859829 344273 895259 756634 893420 156456 439960 890234 550436 385354 167135 378613 912621 079886 651153 967381 324055 243100 448704 105458 609763 516098 742828 371508 862410 906817 875093 307751 822547 802959 495404 101492 552490 497258 468522 631791 119148 819975 328764 042109 816273 842368 235072 601488 371624 480073 516063 545270 567167 525401 252570 514424 402204 500707 636131 295046 861538 168306 543580 742828 562108 580092 265419 771853 377304 443271 869223 129006 492347 707729 947726 057858 650348 276364 010373 150893 171563 771254 288907 250055 667219 724788 582894 837601 135759 114478 823637 635964 095358 625445 843980 282244 844317 773833 731785 447220 157704 543836 960061 964792 094369 915617 069763 570545 655032 560972 163822 < 271344 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27107, 1451, F27, 92) (dual of [1451, 1344, 93]-code), but
(108−93, 108, 1454)-Net in Base 27 — Upper bound on s
There is no (15, 108, 1455)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 107, 1455)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1476 381303 457801 976266 541796 722150 690101 997161 658751 707819 181616 778945 201095 377358 172324 747061 612438 136200 052487 516709 568895 453975 629614 760050 566859 506485 > 27107 [i]