Best Known (110−95, 110, s)-Nets in Base 27
(110−95, 110, 96)-Net over F27 — Constructive and digital
Digital (15, 110, 96)-net over F27, using
- t-expansion [i] based on digital (11, 110, 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
(110−95, 110, 136)-Net over F27 — Digital
Digital (15, 110, 136)-net over F27, using
- t-expansion [i] based on digital (13, 110, 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
(110−95, 110, 1446)-Net over F27 — Upper bound on s (digital)
There is no digital (15, 110, 1447)-net over F27, because
- 1 times m-reduction [i] would yield digital (15, 109, 1447)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27109, 1447, F27, 94) (dual of [1447, 1338, 95]-code), but
- the Johnson bound shows that N ≤ 14 217619 108430 063400 818093 561815 446080 448503 974404 583055 164734 944369 165641 140877 309810 353869 485427 008519 373353 728540 936344 862167 457191 683765 689427 004925 190211 243990 738471 493382 095239 009472 926857 259698 498474 856813 341095 068617 655167 626107 386692 574805 641136 702563 393646 308757 469153 799064 307724 789898 410235 694299 358571 113673 390043 401185 472999 072373 772772 601659 111929 761954 784903 398736 398457 130218 579122 494867 821364 731517 200237 741646 029541 204908 376935 979865 446097 958776 441687 347556 476635 192947 644742 727528 021622 569999 405205 451669 101165 805600 066572 280992 149241 081946 693513 909725 890014 978951 752425 925954 533438 340553 281672 200760 029317 518454 965292 725722 083353 475578 777525 668207 963752 027542 604009 843785 986121 073289 467920 339242 677646 983958 512306 001986 566451 570808 831684 767752 524278 009661 616340 987157 402484 833493 524041 463762 418355 971372 866730 455538 829766 045014 302007 496285 314649 047191 102745 363360 949264 226171 199125 200587 090906 213125 018276 567929 953285 935542 249580 701272 097951 122827 476161 331837 132417 600951 481993 072765 613583 593853 623882 144911 061219 998484 078469 751503 231229 936478 580135 546953 127007 675377 458298 652601 694765 433296 606033 687759 951103 193892 466470 444418 533990 818346 859829 169925 266751 616202 239100 980790 459895 517368 290241 020533 495588 705040 393606 237967 944009 878497 119976 170393 687361 323375 548084 683372 053707 057141 031568 475553 713332 323299 193175 783405 539765 285347 197980 727221 143629 825905 932938 246738 275200 570319 498370 473769 382692 123506 503354 015052 725911 212691 840421 590533 188937 780535 306564 253771 937392 662317 044257 964561 247208 600110 127948 909980 162907 978073 044551 469775 826656 994495 723201 088662 559077 056279 996291 097840 362627 221689 942999 396645 663158 817993 789990 557136 936405 929183 909510 406412 576471 672824 492613 077371 192295 245770 560786 220283 035965 891039 146131 906860 884112 991407 340722 388142 460623 325902 734222 566364 356708 684543 066371 345107 677686 268040 297686 523879 014526 644857 262345 088043 084062 051669 607025 525818 555984 983958 771625 572572 < 271338 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27109, 1447, F27, 94) (dual of [1447, 1338, 95]-code), but
(110−95, 110, 1449)-Net in Base 27 — Upper bound on s
There is no (15, 110, 1450)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 109, 1450)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 048042 804081 237858 155735 021632 946593 378711 321686 152129 287583 144280 774497 017467 670352 180027 127538 882604 421653 601576 137628 358527 495056 366761 100813 559074 631209 > 27109 [i]