Best Known (96−83, 96, s)-Nets in Base 27
(96−83, 96, 96)-Net over F27 — Constructive and digital
Digital (13, 96, 96)-net over F27, using
- t-expansion [i] based on digital (11, 96, 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
(96−83, 96, 136)-Net over F27 — Digital
Digital (13, 96, 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
(96−83, 96, 1262)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 96, 1263)-net over F27, because
- 1 times m-reduction [i] would yield digital (13, 95, 1263)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2795, 1263, F27, 82) (dual of [1263, 1168, 83]-code), but
- the Johnson bound shows that N ≤ 6700 740776 363431 098203 845520 319860 216576 152576 409734 864730 234256 415464 019867 063849 343263 080577 081832 004321 467083 146496 911109 762576 190970 841960 016124 046629 573945 512877 091027 271511 806901 416209 414404 686001 233102 579319 892288 827660 807400 514434 356908 764553 581784 696714 181876 963812 756459 861172 299892 027318 692191 521160 976246 069798 946616 308187 732436 972126 833710 205689 262019 269058 849511 554264 861971 547020 951816 047870 197438 879403 304143 135683 753571 791565 557994 416545 398652 485768 655571 100052 532486 134923 584940 899986 254834 400261 181441 398492 178858 098938 187732 105554 183024 533428 768405 701368 042662 634282 508765 981807 651931 911731 163833 772848 355401 785956 411384 015428 612235 160631 896504 066966 396847 573453 369635 493371 815003 610736 696901 818369 609777 050316 081393 947552 506875 413393 440834 761402 321078 975682 698937 963520 648391 019173 387308 163243 891097 074857 616276 454613 851153 494923 124160 219976 832458 224810 888977 955553 481209 562362 254752 608483 251357 802114 126578 785888 187302 387063 264467 233630 576023 620607 341722 965698 428260 493798 662546 928152 425244 430847 854880 794980 657944 357087 465397 961369 429706 223557 433639 081570 679076 492774 958630 291940 536891 373111 961626 169775 005041 181445 251808 210773 886986 363228 660081 475765 941546 552638 863967 443955 617396 522487 617010 184848 958998 274358 191141 171471 755408 128511 876471 549309 894958 090985 117977 742339 600001 237419 279056 086719 131442 155615 153934 226638 283270 947215 143225 269769 879942 285272 063390 712041 309148 132967 984866 896932 121215 414008 771640 538437 598014 918607 177831 708187 845437 746015 643662 563143 165809 805136 731553 228147 610116 769422 661114 464433 874244 015013 786119 634539 015089 386323 744163 641137 469409 218442 258888 006264 346645 037903 227705 827373 977763 059807 354633 644918 666392 856136 981704 < 271168 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2795, 1263, F27, 82) (dual of [1263, 1168, 83]-code), but
(96−83, 96, 1265)-Net in Base 27 — Upper bound on s
There is no (13, 96, 1266)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 95, 1266)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 9751 669378 090587 652952 915672 709555 801705 645830 439040 461420 569726 902090 081279 423287 927824 613083 056617 678391 169508 479538 552930 722614 692997 > 2795 [i]