Best Known (109−95, 109, s)-Nets in Base 27
(109−95, 109, 96)-Net over F27 — Constructive and digital
Digital (14, 109, 96)-net over F27, using
- t-expansion [i] based on digital (11, 109, 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
(109−95, 109, 136)-Net over F27 — Digital
Digital (14, 109, 136)-net over F27, using
- t-expansion [i] based on digital (13, 109, 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
(109−95, 109, 1347)-Net over F27 — Upper bound on s (digital)
There is no digital (14, 109, 1348)-net over F27, because
- 1 times m-reduction [i] would yield digital (14, 108, 1348)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27108, 1348, F27, 94) (dual of [1348, 1240, 95]-code), but
- the Johnson bound shows that N ≤ 75323 909680 636030 423894 626856 717026 905781 679222 061849 099631 725403 581294 825534 498004 388387 760198 395736 350346 996466 316570 647036 407030 956711 627778 842763 987931 934731 343794 338809 889369 073330 853239 406047 914530 889888 154787 810354 590891 300492 056625 419856 924642 662111 271715 733075 678635 068368 389549 755821 598451 387876 612009 640882 496719 595564 788543 372537 275966 030305 900477 316117 831610 217282 109628 586761 206712 156789 253125 111031 480700 383799 492369 160865 555682 764013 958263 533908 582714 718616 695328 149779 856820 164155 762264 066440 332621 609190 989246 243976 031416 026823 121332 927914 030853 981886 313827 484776 119392 608236 956232 990113 696010 821167 682865 159102 868390 295814 273547 660099 121211 561436 837587 900774 282434 031247 174485 790516 605047 127689 633556 143287 513934 852275 887252 619717 334076 306087 244638 260400 382539 372983 901082 836509 491409 118092 662262 253017 379650 663206 421954 191882 492209 416669 434520 809456 824989 815745 854042 687510 753108 526683 422652 694442 675196 238918 777514 044137 043080 569150 792592 106748 475608 985473 397242 098497 457562 220077 936167 211307 968596 905009 869546 331081 335398 139859 670800 399475 978706 102000 690777 721872 160700 986929 959097 758285 455413 879343 481416 189465 323325 464732 245050 376495 260843 335701 793604 744096 761422 677911 144526 543384 712696 909040 483551 463353 992675 147695 304976 130074 841616 800967 734352 109639 197930 105454 625209 530915 081466 602820 202128 365120 292460 439267 109735 954171 111096 143199 871784 330220 895811 803288 738027 285098 902658 899982 166058 351399 579688 303619 395159 394761 819575 409856 013276 512015 136901 827952 455229 498369 584880 953420 241602 752317 222330 901660 334529 276968 330103 393463 199972 046195 149849 332317 676276 541625 941782 945384 074703 575530 558341 109135 661323 680329 343589 525236 393023 710794 601244 931777 776018 801803 296901 253738 944614 677605 003042 494907 703319 932196 914753 386962 020698 704193 864664 424320 448470 < 271240 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27108, 1348, F27, 94) (dual of [1348, 1240, 95]-code), but
(109−95, 109, 1350)-Net in Base 27 — Upper bound on s
There is no (14, 109, 1351)-net in base 27, because
- 1 times m-reduction [i] would yield (14, 108, 1351)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 39979 816572 023613 473872 713717 947110 262808 810128 752949 774812 087172 151590 733770 060668 566887 230197 842170 165584 803089 172342 345421 414178 532992 218803 900293 061019 > 27108 [i]