Best Known (14, 14+∞, s)-Nets in Base 27
(14, 14+∞, 96)-Net over F27 — Constructive and digital
Digital (14, m, 96)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 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
(14, 14+∞, 136)-Net over F27 — Digital
Digital (14, m, 136)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 135)-sequence over F27, using
- t-expansion [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
- t-expansion [i] based on digital (13, 135)-sequence over F27, using
(14, 14+∞, 417)-Net in Base 27 — Upper bound on s
There is no (14, m, 418)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (14, 833, 418)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(27833, 418, S27, 2, 819), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 143955 957216 464837 647688 703299 548113 462623 745288 507452 976986 587685 264149 338646 494028 860433 386480 502756 751482 560263 253929 308874 340099 948862 472880 254270 252844 875662 358396 507130 010156 088753 463787 978247 540110 391717 031008 299352 395708 418806 370153 707938 855073 928393 530336 421966 605707 742006 313967 954289 957514 113616 369778 410015 730205 302307 000471 135406 665582 638831 228594 472286 723679 112423 568257 317776 715864 765436 615178 402237 684331 853670 683951 051415 276734 227025 396247 606984 625483 634894 541700 141104 567622 458138 445642 732338 391157 858812 526832 557905 910584 044483 491912 367266 793760 531225 781569 234249 757778 889453 733855 230025 473924 002607 467141 270758 437077 810848 514433 681575 039781 462433 584026 070051 197212 058655 530167 940899 530377 619382 573737 828549 834628 899228 224580 664147 143200 858433 983076 416250 843947 938391 020533 517235 322741 362140 043087 424060 421597 641190 036892 272082 651409 047132 507236 227348 751931 662941 850199 119512 711730 547779 388012 561614 853731 083069 584602 577082 172046 960841 923193 986586 167707 742541 111873 907230 237505 684481 824635 012863 623051 707694 466939 164637 048955 641628 123620 446687 296156 521337 086083 170418 106632 453007 375407 219625 081632 959067 481003 179830 367679 808351 622565 990509 297075 580116 654873 635237 761984 900018 / 41 > 27833 [i]
- extracting embedded OOA [i] would yield OOA(27833, 418, S27, 2, 819), but