Best Known (30, ∞, s)-Nets in Base 81
(30, ∞, 370)-Net over F81 — Constructive and digital
Digital (30, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (30, 369)-sequence over F81, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
(30, ∞, 551)-Net over F81 — Digital
Digital (30, m, 551)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (30, 550)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
(30, ∞, 2542)-Net in Base 81 — Upper bound on s
There is no (30, m, 2543)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (30, 2541, 2543)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812541, 2543, S81, 2511), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4676 791246 950606 298885 533417 789961 350348 362174 730570 945604 181671 971985 493376 852718 667446 559417 939756 070938 185409 061280 078049 471814 374186 561342 057009 542406 247355 661340 410103 584052 140934 716335 121473 617333 433207 365391 607439 301190 821354 439246 033908 694991 067672 863597 984023 444781 888432 106731 610947 257320 795579 542471 446463 944917 275121 281949 192435 607059 068974 832429 412523 438730 634760 496764 882387 991478 335120 250515 733825 891076 106126 310707 923199 159864 498025 690847 148937 967098 549131 108213 601753 869789 640195 812840 149986 716278 390352 857861 631770 073106 058129 482390 937736 811612 590381 590141 293997 618057 827810 175585 829999 739785 470130 129306 860435 710090 404272 240307 116630 998643 012090 690514 827802 899467 564511 352166 655434 750807 942259 076795 467076 393522 564181 634014 339031 772986 478532 612479 493596 281477 855075 983161 051836 718226 624020 222014 344117 224104 431101 273897 223611 211224 567870 548201 471484 964001 840261 391778 665557 994501 558493 525393 726294 835128 010641 169328 420960 968176 789821 243030 406297 153077 902473 887705 386131 021401 817791 519086 180061 796572 028442 426184 313204 400528 583439 616764 380973 112214 227655 368836 786986 047171 295663 431814 123781 747228 153716 742418 549954 568504 072418 550585 729286 672797 928055 533796 391840 131813 090085 482229 739584 522916 221587 117835 163314 399670 037981 732992 062758 431218 564399 348719 801361 637252 430363 843564 422083 314852 870918 890378 892112 399295 853473 249428 019863 114087 251167 021202 668192 210511 738634 968531 348337 776181 162334 299220 832273 053769 732740 957377 446367 261434 492093 261506 373215 005269 113534 618264 874745 952018 718056 430089 222710 049918 838988 539795 958035 707334 920974 289078 522947 417264 834794 848164 774773 244035 297134 316708 275142 011828 414501 941085 757165 933202 338340 443126 120270 903476 547214 354122 670767 686670 486416 213808 085657 672313 893918 338333 156470 731916 545249 449734 056973 958834 865198 399959 066644 317871 796345 024188 970281 639865 650473 061312 642776 760856 644016 151322 251774 438468 776666 866122 278467 619102 246080 008062 329761 217937 387561 099268 523289 245880 354133 242528 344924 191940 038412 595358 942060 779015 925349 328280 084061 643266 066177 908131 016838 100719 605424 845179 238404 416494 804183 292556 516187 838831 441848 817345 122873 355917 467658 803290 605130 519924 911915 320519 558142 098906 561977 028068 761657 434739 361592 046357 460898 637294 494131 462651 144715 790917 914738 257655 261948 049192 535407 150580 379842 890654 527618 702514 601569 331592 084434 296954 370715 481137 805635 416115 984176 771582 565676 722110 978794 347752 964455 124306 959629 142878 325725 478679 086480 629758 117061 951385 944349 353767 436407 088018 146631 501028 791943 423369 863759 816477 489420 617459 099165 585926 143841 053385 112178 536475 081303 101097 131187 451545 158010 234813 397180 464026 273934 159798 846255 607669 328277 319838 664171 509017 780308 984990 611410 973103 610835 622293 187730 080492 498651 601829 644756 683902 597961 521332 942520 845628 455202 326257 904531 230803 941013 552822 969789 743999 854709 039183 492924 281632 997717 703782 023962 639394 802886 877690 882475 324791 692424 005494 732020 927989 711756 528099 939122 196576 799270 559066 992463 056654 409376 245597 364820 103141 622910 224972 282954 974665 725716 621521 923654 140551 094118 295265 430364 347731 478380 611093 575829 351886 667470 762286 332784 144289 441962 169449 273041 220471 412881 195330 688503 441534 466967 114863 502436 470026 737827 284968 238657 869405 057898 956275 079916 086578 631694 073983 044550 060767 148138 259075 736499 819327 155634 900044 447615 087668 526399 160987 243941 933086 038095 040486 633327 499102 965924 340725 393775 280233 698272 255733 028873 959253 249018 067514 583273 916134 760317 455407 368618 453689 272716 957931 548148 198021 476444 178734 029692 965361 012291 081726 048608 841268 578926 336091 711525 835184 105037 651796 519431 145952 178404 731511 578549 753539 385873 132617 247841 865156 411804 823206 145450 812502 364649 070746 912777 998336 726263 743039 745128 993768 410231 592073 773761 055101 960821 525409 612300 353976 924311 516507 305823 871343 268161 914448 758205 595080 562176 470329 489229 538351 171638 605441 839122 797655 451238 987936 861299 267469 208657 467381 251275 250016 688936 330541 000526 676219 683171 005124 262903 594354 462090 746031 264011 623888 110139 259948 642238 556908 265901 794112 698996 780409 181948 179581 343700 064395 674411 478921 773261 144025 897522 533793 891572 123275 632721 167210 916925 834040 954089 221761 336065 003478 070900 715834 434668 746035 427016 411104 331683 558234 749207 475758 044597 364893 222817 489144 036659 609278 532937 404892 085355 202699 180115 321715 580483 621792 077115 846228 068556 993577 096371 743996 632994 281035 930987 494952 791353 129043 804056 444391 276990 614477 134554 529141 948374 697652 751996 083858 198644 878467 461632 162305 835894 525976 833834 491096 991752 410580 892561 756576 596586 321291 643039 545827 078398 246845 702668 360892 633000 385083 138787 603920 120739 406004 340895 731682 354956 031031 241985 278749 047464 016993 455080 770521 420997 109898 477309 847247 659174 708830 689114 641943 284457 820716 722001 886630 705257 941297 873568 729898 634907 002113 756658 148841 615060 473259 854295 162970 582700 846713 059910 791889 858780 943818 999941 456750 227175 373998 736787 410892 737785 281440 719025 313949 415339 091633 430238 569030 083587 129356 576478 552013 347522 / 157 > 812541 [i]
- extracting embedded OOA [i] would yield OA(812541, 2543, S81, 2511), but