Best Known (104−90, 104, s)-Nets in Base 27
(104−90, 104, 96)-Net over F27 — Constructive and digital
Digital (14, 104, 96)-net over F27, using
- t-expansion [i] based on digital (11, 104, 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
(104−90, 104, 136)-Net over F27 — Digital
Digital (14, 104, 136)-net over F27, using
- t-expansion [i] based on digital (13, 104, 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
(104−90, 104, 1350)-Net over F27 — Upper bound on s (digital)
There is no digital (14, 104, 1351)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(27104, 1351, F27, 90) (dual of [1351, 1247, 91]-code), but
- the Johnson bound shows that N ≤ 803 266668 136326 117109 272698 313444 916270 664912 057406 527661 746063 753005 869398 702947 552220 506217 655901 520213 283980 942792 188714 356932 048692 646971 528261 707122 938444 762515 625975 818975 099277 791368 091893 041505 025564 436932 480151 735947 604167 905534 745572 749709 078437 207182 375818 778235 677281 403694 576656 381827 589734 662240 444336 942086 974383 242202 915846 577776 395983 245332 047168 935657 817919 987572 716648 848554 605980 543502 447551 363099 502109 202730 213498 398176 690675 572867 792514 623954 221965 552832 730609 087223 494704 548340 134645 728483 963018 747625 453430 704867 817762 192329 831642 050509 605279 013085 524983 541678 596824 255439 170650 215757 710834 062132 993297 967796 516016 203057 918602 567871 037865 950225 078163 986092 001991 572502 131796 032708 031283 245678 783866 561004 444833 129531 098489 974740 926400 631479 938037 926694 667126 790380 102862 821469 222966 187823 147763 220666 180573 044459 859164 693277 740915 102058 969528 637710 216393 969749 214205 273475 165494 692292 247070 857245 448480 525828 332824 737260 907150 966543 812625 076823 275759 130533 750758 150717 747052 473868 694129 348327 902346 646953 458745 854301 890808 961092 791861 457178 162125 161521 712546 397694 095888 813989 541396 294426 717357 436013 421325 354373 956190 617572 707532 441031 391584 652119 889191 864662 328264 994587 145235 837064 072797 483014 293922 398716 073546 718566 393939 586982 690795 459947 009146 291742 225115 630793 946272 523442 970174 219563 066046 218745 821344 723358 595943 310710 254340 414021 436638 265424 436410 512843 794479 416353 517209 170945 268786 537059 534761 408290 912296 032066 434469 983283 219660 866621 954502 643814 376449 145194 703618 951177 926659 267757 128741 245736 751915 013247 992410 580917 801855 822415 340885 151759 574170 840374 697995 333868 693129 428471 566806 362185 309511 199542 541067 701144 307264 852239 492261 481606 772385 917527 686653 119191 683218 319391 874241 723575 989443 897975 261525 863610 042501 530348 012867 890732 502512 342700 < 271247 [i]
(104−90, 104, 1354)-Net in Base 27 — Upper bound on s
There is no (14, 104, 1355)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 74352 511793 378879 833422 040752 685083 195747 063308 541103 074058 411104 175871 309076 835356 293595 905173 916797 725584 696052 829399 543034 758041 017414 162150 896551 > 27104 [i]