Best Known (106−92, 106, s)-Nets in Base 27
(106−92, 106, 96)-Net over F27 — Constructive and digital
Digital (14, 106, 96)-net over F27, using
- t-expansion [i] based on digital (11, 106, 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
(106−92, 106, 136)-Net over F27 — Digital
Digital (14, 106, 136)-net over F27, using
- t-expansion [i] based on digital (13, 106, 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
(106−92, 106, 1348)-Net over F27 — Upper bound on s (digital)
There is no digital (14, 106, 1349)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(27106, 1349, F27, 92) (dual of [1349, 1243, 93]-code), but
- the Johnson bound shows that N ≤ 1495 008515 348889 677205 444834 420129 088412 266717 990911 253311 886625 171239 175318 994083 867787 376289 038829 331382 670895 837899 170533 199337 546888 177905 695192 250830 136209 866148 384173 088604 848944 686032 712815 785929 302479 274529 975576 553915 970122 883513 770635 353792 802886 994116 193560 947948 165117 062856 189604 998215 487718 355591 986968 238680 248235 661923 751307 594510 806687 570675 614949 880090 735278 956204 961815 015278 377214 761912 383156 812220 210169 499730 593161 186353 827960 114272 519672 972271 935344 196503 091189 370485 562870 733780 482350 736751 477931 828375 208976 889684 343467 139578 285106 443483 689138 703967 124356 701395 785519 521639 616438 826143 956117 077709 821039 110509 549835 929773 751093 109149 765576 343374 941037 543746 520484 860776 734194 433207 819819 636887 545893 403286 597048 169130 247437 637978 163643 602757 190044 524863 286166 455015 527812 052638 617957 005886 830861 907525 869440 551797 175060 957983 669837 819635 871614 518636 403511 428533 659382 314057 809523 721646 926240 451935 490967 028997 949637 581133 358917 762358 727867 298678 350167 375221 743296 211374 416408 670489 131057 644446 281436 847705 296260 160400 483101 478181 533653 986603 884361 881954 732200 747417 706819 291237 820820 595352 243025 153286 448010 945918 149577 868849 380275 476489 790101 041082 783584 969174 755082 051192 127334 314401 922410 862500 901500 817811 578797 077121 747814 035716 166020 660886 917135 108698 757750 818473 909582 154156 567546 402661 484879 093302 235332 688007 636053 687233 439297 446237 822194 938799 798297 960934 729501 182311 491691 773990 041289 656759 865867 689903 880135 891715 352758 745745 074607 065783 712789 020685 759763 415183 350455 948516 756074 075960 316745 603115 413569 784643 514966 045852 973052 945730 501476 678571 257136 947388 351267 193665 355503 048957 360152 024040 241157 666739 430350 284260 707927 258815 446619 702748 810038 571686 960482 036153 741626 265817 783346 926059 221343 106771 014288 087219 091477 694932 717810 092853 645835 < 271243 [i]
(106−92, 106, 1351)-Net in Base 27 — Upper bound on s
There is no (14, 106, 1352)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 53 358061 762771 662984 455689 462582 399046 054215 926261 454827 439766 244215 408286 536352 038764 926174 668856 520508 588310 171480 362419 102319 505650 063628 192471 125553 > 27106 [i]