Best Known (15, 15+87, s)-Nets in Base 27
(15, 15+87, 96)-Net over F27 — Constructive and digital
Digital (15, 102, 96)-net over F27, using
- t-expansion [i] based on digital (11, 102, 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
(15, 15+87, 136)-Net over F27 — Digital
Digital (15, 102, 136)-net over F27, using
- t-expansion [i] based on digital (13, 102, 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
(15, 15+87, 1471)-Net over F27 — Upper bound on s (digital)
There is no digital (15, 102, 1472)-net over F27, because
- 1 times m-reduction [i] would yield digital (15, 101, 1472)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27101, 1472, F27, 86) (dual of [1472, 1371, 87]-code), but
- the Johnson bound shows that N ≤ 2 452586 947428 663160 219997 660002 483906 393093 746528 790865 445450 482115 653433 444455 039257 641644 715582 366207 205292 103875 252684 797442 708063 213188 911984 331592 680689 784924 268797 602194 979991 148575 489615 752404 628750 876456 251795 113625 972695 558521 571484 476529 432544 595574 063593 447769 841934 175019 175549 312179 750809 563470 034251 567622 742285 568180 417421 027710 792854 661357 174093 532870 947563 342023 401315 206524 687248 311959 437618 484759 279946 025082 368523 294933 225276 539336 252519 899139 837117 999235 401369 143551 404659 838575 503900 773964 257932 252990 389241 457238 183485 906489 025527 921898 460021 575259 442410 179357 140158 171779 801584 345276 051426 378887 677468 396735 205543 627966 586950 011151 752989 147121 668650 381066 822765 646997 764818 389350 571635 853260 451719 780400 481946 977657 739958 199419 210732 138703 760725 634409 957165 980353 047138 227306 303066 676495 854909 224445 192973 838301 318637 891957 696409 023294 793752 950921 221570 975294 077380 711574 557728 021381 780047 901292 606832 626015 422231 184291 950249 814085 951312 580508 296671 065069 954507 895976 947442 345530 013894 801098 668755 487100 392743 946629 171953 017329 601196 227036 006222 421060 491816 945401 709718 324746 258621 789558 039133 381071 344783 425186 083918 231007 315562 837712 024015 388247 220743 651756 569987 548052 495938 582583 102965 558588 830448 260174 564194 681865 121539 191270 224537 308351 663069 302936 562295 761628 854525 616925 188991 185891 617572 194075 360665 340748 219301 545386 630968 862965 649691 758158 051954 247038 373584 274067 598997 565249 160374 615484 296731 897104 514296 579416 347722 985650 292561 676294 322402 810616 003726 138168 414414 307973 188323 627610 818108 547864 432618 868741 476491 281599 978164 501444 804410 423808 482526 614241 303060 436434 651134 120993 762040 217356 055670 080750 449399 365072 872162 698681 499607 550597 336890 309933 244170 442668 340927 147590 318732 331382 031943 689049 208114 968299 371068 555543 320336 736838 675135 909403 835324 550881 717891 880146 917144 996197 130492 561829 475106 701295 718701 558607 335442 701766 832407 799911 347304 083781 974397 081846 945738 825572 539952 811043 799149 556005 372595 641177 736894 790866 < 271371 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27101, 1472, F27, 86) (dual of [1472, 1371, 87]-code), but
(15, 15+87, 1472)-Net in Base 27 — Upper bound on s
There is no (15, 102, 1473)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 101, 1473)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3 797547 428214 592393 570070 006108 050811 506946 326916 671108 095535 396523 467352 957047 703523 641365 634042 036962 974300 717417 991061 447711 026709 195364 279555 > 27101 [i]