Best Known (17, ∞, s)-Nets in Base 27
(17, ∞, 96)-Net over F27 — Constructive and digital
Digital (17, m, 96)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 95)-sequence over F27, using
- t-expansion [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
- t-expansion [i] based on digital (11, 95)-sequence over F27, using
(17, ∞, 144)-Net over F27 — Digital
Digital (17, m, 144)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 143)-sequence over F27, using
- t-expansion [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
- t-expansion [i] based on digital (16, 143)-sequence over F27, using
(17, ∞, 495)-Net in Base 27 — Upper bound on s
There is no (17, m, 496)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (17, 989, 496)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(27989, 496, S27, 2, 972), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 415 267785 068256 181624 761136 478849 407236 039749 721608 091368 290626 780864 831389 774150 600876 348522 282949 219495 090674 134032 648146 072162 420186 033508 963490 911732 601274 528833 886159 387265 038615 682455 976347 289516 719466 492666 954867 831650 391192 914344 368176 987298 932106 080058 307446 393638 392101 365504 628198 157643 129588 337067 802148 772041 779610 502615 292153 469501 602543 240533 652145 953418 453135 684730 061013 359624 839691 945075 700032 791739 173134 159547 856980 246483 981516 301335 802142 272924 091561 611716 289097 446876 582854 327794 639874 553373 942939 266657 965041 757291 046949 846747 542020 068209 853299 660012 402384 881052 174941 466829 350541 990140 846163 496597 163912 436089 009441 287579 633784 442608 508932 780449 894985 564785 262802 334265 169941 774581 461750 386957 225581 565005 376612 259655 163495 507449 889786 319474 482831 619319 283776 368914 462743 364187 506189 209144 230863 717823 604372 102863 535352 222514 523722 248203 913596 448378 854861 397371 309035 236254 049029 427082 500092 924241 989101 336449 142572 255880 355715 733318 504826 633619 224797 011315 683646 429961 803963 325771 505059 759050 310984 023322 549752 121928 247985 334825 909760 087641 370805 664333 028940 502194 803031 877462 705896 944988 887151 717577 231975 240436 413007 585660 232716 443762 672635 151041 057146 507566 333121 239292 914391 860675 637327 187969 309317 015620 148128 263432 508988 420134 283204 606491 893634 601162 350306 371041 339645 702545 325828 077825 386193 853347 493581 587046 017378 312086 892774 995241 005781 441732 365125 621862 975437 047877 228449 423716 170413 / 973 > 27989 [i]
- extracting embedded OOA [i] would yield OOA(27989, 496, S27, 2, 972), but