Best Known (13, 13+87, s)-Nets in Base 27
(13, 13+87, 96)-Net over F27 — Constructive and digital
Digital (13, 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
(13, 13+87, 136)-Net over F27 — Digital
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
(13, 13+87, 1255)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 100, 1256)-net over F27, because
- 1 times m-reduction [i] would yield digital (13, 99, 1256)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2799, 1256, F27, 86) (dual of [1256, 1157, 87]-code), but
- the Johnson bound shows that N ≤ 1 216457 362237 873358 779605 433668 609226 306254 304094 043429 551130 156349 947879 823070 091028 182064 291057 192401 222169 444273 653469 668960 771740 627807 033441 397308 330581 958352 628294 823955 156274 956866 679224 689664 024010 374737 213963 585901 706972 210338 549114 566667 287825 876875 780527 116531 658908 894829 964738 445043 071853 488808 992037 530371 282761 051328 584935 371163 165589 721724 809590 212652 510566 593243 777830 458948 212124 644442 439960 213778 657008 003938 288026 866182 531346 094934 014239 968983 299570 733606 485817 112531 730356 014795 714133 501126 428041 773923 805440 553245 995019 036481 127187 244595 338767 561201 123472 099294 945786 338164 391641 967958 619932 859402 722315 078936 363159 418906 653706 305484 094045 229002 021527 216998 292228 720517 198162 851998 490548 997236 179618 291897 350856 313087 356713 516711 608103 539199 217692 156543 794943 358248 996543 924968 794059 724537 785840 194708 356474 964207 692306 421304 093082 335943 800858 629452 919507 194382 167417 587352 310328 425926 394867 694659 821119 013189 097376 586012 703683 483802 811980 630300 727444 177469 458896 482947 099856 728853 497545 060380 187240 444751 560677 736360 936681 011580 716725 308274 247687 644699 459709 616524 695324 625746 318537 440255 184593 395934 441928 312694 731575 329080 973875 129184 524319 891058 671941 825744 223571 518925 824002 544215 505314 283212 783442 838146 704559 319748 326634 127585 354405 148598 531795 834714 962676 841480 422411 010886 924304 248418 480286 912540 462143 810812 100413 867113 599017 350143 169221 018965 138702 445372 741415 641496 792120 133646 440727 231028 009301 134221 790691 737881 314403 582978 579527 680519 926162 316755 969130 026840 847101 445276 140091 440500 489361 903097 509384 726248 691611 232314 521807 153136 815322 181695 008942 068874 797615 195290 264615 385812 678246 524216 525528 995287 623356 176470 155583 < 271157 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2799, 1256, F27, 86) (dual of [1256, 1157, 87]-code), but
(13, 13+87, 1259)-Net in Base 27 — Upper bound on s
There is no (13, 100, 1260)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 99, 1260)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 5130 213964 750757 167147 958031 465892 159441 208028 881963 638104 030913 139708 148913 363326 997572 263540 414769 208367 592395 466589 851872 207229 743862 166705 > 2799 [i]