Best Known (101−88, 101, s)-Nets in Base 27
(101−88, 101, 96)-Net over F27 — Constructive and digital
Digital (13, 101, 96)-net over F27, using
- t-expansion [i] based on digital (11, 101, 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
(101−88, 101, 136)-Net over F27 — Digital
Digital (13, 101, 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
(101−88, 101, 1254)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 101, 1255)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(27101, 1255, F27, 88) (dual of [1255, 1154, 89]-code), but
- the Johnson bound shows that N ≤ 60 766695 919869 974178 719762 516225 937380 222411 085373 933667 961111 371034 629974 454599 726819 702057 138910 167339 994619 789283 234436 997552 946286 135578 526436 564015 005294 057569 777252 222113 737634 934676 674337 769912 813360 615311 961917 884653 857160 258741 371264 534531 765477 709240 957645 376269 492865 675191 532392 707423 348352 385402 376095 707231 068633 966197 793640 012045 079095 873396 104405 888618 763304 390865 045993 280960 522495 216737 868207 382925 980132 052397 494994 915764 915688 016152 093609 854513 233884 613601 660746 412484 303774 123280 515421 041283 021759 026611 206637 864294 253512 939657 264452 939173 404021 645375 312553 802801 971309 918734 883519 050033 559127 879209 865691 966730 669437 191317 831233 305921 678236 309887 839989 829256 292727 788008 376339 844898 667552 700054 530481 765134 012458 766616 936827 495416 171369 746619 461586 353022 135596 050165 456306 280822 115289 930439 557351 227545 499094 481547 277322 740117 692383 735012 880437 960402 219281 045583 081613 561676 113010 311492 220912 449298 183122 754884 771846 726658 699538 458928 346759 605960 654100 194607 581544 193329 303359 280190 630660 339786 249306 781165 298084 622903 179738 245196 838876 012585 543354 016586 523405 687820 247763 827293 411378 611949 532934 611048 619362 849876 434918 341510 445938 812110 594117 051523 933785 538505 039595 874827 864717 886347 598407 979130 325869 890832 220681 872243 208707 454278 882812 374684 441490 662844 754219 783074 183286 486858 565500 571932 156678 385931 805343 579336 281161 472408 007840 946439 926197 494249 469861 474397 668325 331342 809509 186027 773395 040998 454372 420057 255072 812581 957589 116075 041283 228916 648056 446102 828944 348235 117321 936199 461579 427484 808826 946025 193632 105056 388604 526447 626714 590601 177220 035248 291972 447862 923825 897660 326699 951539 046842 486990 751371 648476 514940 302377 < 271154 [i]
(101−88, 101, 1257)-Net in Base 27 — Upper bound on s
There is no (13, 101, 1258)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 697299 556735 181481 716552 001180 294208 404216 500098 339637 073455 006709 673963 252909 817961 166307 711683 776261 019080 430496 824653 304395 293196 943684 645305 > 27101 [i]