Best Known (14, 103, s)-Nets in Base 27
(14, 103, 96)-Net over F27 — Constructive and digital
Digital (14, 103, 96)-net over F27, using
- t-expansion [i] based on digital (11, 103, 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
(14, 103, 136)-Net over F27 — Digital
Digital (14, 103, 136)-net over F27, using
- t-expansion [i] based on digital (13, 103, 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
(14, 103, 1353)-Net over F27 — Upper bound on s (digital)
There is no digital (14, 103, 1354)-net over F27, because
- 1 times m-reduction [i] would yield digital (14, 102, 1354)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27102, 1354, F27, 88) (dual of [1354, 1252, 89]-code), but
- the Johnson bound shows that N ≤ 11625 033083 106652 446840 477928 929828 965886 406080 151746 928918 877394 899306 564726 028396 979532 323126 613944 098161 102460 184136 997238 726860 962975 123510 053500 114924 915040 386107 108434 194224 855100 482040 758020 215147 684731 451123 566891 994581 788866 052679 866096 525423 200235 579011 483772 918381 831502 691597 391857 867288 809751 535191 519768 266308 055237 526139 871226 422693 124385 367766 135534 530075 330680 980811 143738 848453 099144 642970 803245 201929 711519 934004 592497 738741 257497 607726 873155 885883 410748 059584 721325 128633 186364 190839 248032 845754 616906 718371 879457 752492 089280 319495 468099 062753 100560 511132 067385 288513 256941 551093 180900 113953 646478 543185 528881 607505 068734 687627 840688 625177 997840 295109 818522 422196 046182 564405 117388 855629 583406 523882 679259 472212 837733 465858 373452 849468 869349 019572 820001 231171 028304 064578 945588 726434 520511 919955 839588 920345 852177 811361 890713 292135 617416 752601 641454 099844 520221 358899 628306 108746 536226 501718 835830 944969 043062 620867 506819 421983 912594 320162 055253 668690 940453 068509 154237 094877 022678 403716 596291 414239 126737 100518 929957 781938 267052 591922 659600 358971 881257 715209 421906 299869 055385 592861 504060 914781 414233 512629 830086 802711 314550 377082 897286 050768 350096 021249 854694 038384 484824 366518 163420 267602 221569 234645 166946 653875 818693 959696 184218 662764 595760 013116 927394 577439 042840 364875 704151 623219 604249 815829 268119 711707 354037 061543 542201 174025 053996 338042 764210 942573 576113 828219 265669 582874 111849 280310 241225 255503 164817 209482 325565 130417 016745 537567 921350 389348 885608 531304 069817 770165 254391 815433 834739 450575 245873 573640 273496 505351 073736 095224 445045 485167 201326 002276 064202 487649 728339 054405 918009 910922 962807 461613 009007 013737 560680 268502 467343 578380 702008 086843 698208 520925 838993 069428 455320 703877 826865 045337 218273 950502 396989 727740 431138 399849 127787 031807 914072 188622 403414 < 271252 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27102, 1354, F27, 88) (dual of [1354, 1252, 89]-code), but
(14, 103, 1357)-Net in Base 27 — Upper bound on s
There is no (14, 103, 1358)-net in base 27, because
- 1 times m-reduction [i] would yield (14, 102, 1358)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 100 978400 043250 683140 089672 750154 879637 491031 388257 310626 387384 307034 679114 076559 778017 262981 932368 894065 230224 773360 876918 651289 283539 150257 132825 > 27102 [i]