Best Known (104−89, 104, s)-Nets in Base 27
(104−89, 104, 96)-Net over F27 — Constructive and digital
Digital (15, 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
(104−89, 104, 136)-Net over F27 — Digital
Digital (15, 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
(104−89, 104, 1462)-Net over F27 — Upper bound on s (digital)
There is no digital (15, 104, 1463)-net over F27, because
- 1 times m-reduction [i] would yield digital (15, 103, 1463)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27103, 1463, F27, 88) (dual of [1463, 1360, 89]-code), but
- the Johnson bound shows that N ≤ 444 154187 934959 424903 481503 721231 562875 950729 779131 796660 023283 393147 917828 200673 549403 419142 344944 871297 571493 171035 679376 130361 777342 629523 186021 523306 724722 382825 549619 708566 027628 097577 540015 238775 228244 869036 771731 562201 423450 272676 083173 780253 335573 454050 558443 599049 662243 213354 140094 897870 712490 482925 070709 664708 943598 270230 103434 298044 572092 258278 448844 369419 934533 804388 916052 359522 090770 447700 676753 387733 922195 926557 638635 980778 989366 644287 135631 319653 835473 517405 293323 200732 119388 563899 264624 291541 156826 393744 038963 065330 699502 965222 307017 269504 241458 473887 428731 113915 385826 042777 279587 798786 439567 745501 167984 418340 249918 187264 567436 459678 771486 196322 142874 143338 222178 440520 444881 578127 384347 393403 599545 736374 692287 431688 810603 136543 757291 036721 387384 816988 220868 976962 546190 388469 465252 445027 299425 989363 841350 714445 865220 374990 826550 546315 139761 999254 256610 618633 755007 032198 049744 354347 698615 993041 770094 760459 128708 030786 326623 106252 426162 054878 185162 978394 272739 918850 766160 980502 290371 959308 747284 097162 459086 397931 545426 324469 945496 746694 915965 805912 707949 411954 465444 024742 182422 060911 806987 758808 876475 783097 951961 534442 951267 081489 082631 658382 111582 401998 800194 515199 139091 056471 133168 475866 896166 524693 546399 796297 245109 196549 391368 786008 617320 206181 160800 586348 349333 728865 960684 518793 807055 384817 594247 423916 192501 831128 157333 064709 782003 867460 514100 508632 757109 301030 198378 487530 464369 638184 662307 772831 214230 517360 036518 670144 643438 916105 149967 323014 385743 901537 980571 164856 085853 504970 099194 531538 360054 261282 487177 491271 520392 946021 177649 244339 032864 811205 848254 755059 265300 852429 333482 518053 144132 924515 730096 261330 432103 262129 866289 078713 047556 798836 861231 286429 996185 098436 521179 479106 353894 882358 556611 305798 834893 826740 156916 018471 565043 229638 777341 496580 066092 243638 911471 998390 345015 413739 011324 045289 892392 837807 741117 222493 009515 593240 603045 967328 723807 160606 590329 834480 816957 309742 879977 692201 080157 < 271360 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27103, 1463, F27, 88) (dual of [1463, 1360, 89]-code), but
(104−89, 104, 1465)-Net in Base 27 — Upper bound on s
There is no (15, 104, 1466)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 103, 1466)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2773 609753 470176 155306 781185 718570 510599 669016 003337 974066 951697 854262 749184 223819 517908 022385 757702 077868 814461 741898 656096 175794 571484 018733 527225 > 27103 [i]