Best Known (25, ∞, s)-Nets in Base 81
(25, ∞, 370)-Net over F81 — Constructive and digital
Digital (25, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (25, 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
(25, ∞, 392)-Net over F81 — Digital
Digital (25, m, 392)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (25, 391)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 25 and N(F) ≥ 392, using
(25, ∞, 2132)-Net in Base 81 — Upper bound on s
There is no (25, m, 2133)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (25, 2131, 2133)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812131, 2133, S81, 2106), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 209 615799 283263 697109 079472 357458 847267 098326 415024 403930 205639 234798 268378 115200 301231 510851 961838 245335 290204 085798 283086 863881 348179 527908 827024 001388 588933 407030 201434 734187 232088 867233 263867 564414 862260 473834 481723 730303 947178 938142 746097 948183 552556 781132 596731 230363 501251 914993 163879 216176 118767 090257 518728 399745 084257 914800 254576 132062 252188 961352 254390 018672 382786 868537 166407 226778 986864 927776 788965 618733 713976 428087 939345 453758 143621 185758 268996 586443 814709 236320 337056 643567 134385 035322 118438 435573 010298 943907 495238 210470 035106 968526 088231 277882 286275 454816 261926 750935 190764 080435 080807 866729 754355 488350 033421 594744 158277 377768 948775 868277 928941 595867 524442 747697 401348 906086 198452 249782 745325 361561 898211 697755 830332 544152 335859 496821 833585 218656 779794 825329 928170 969234 810741 585566 321058 993945 670281 877132 566698 288309 970582 035980 108205 992375 009794 202257 152586 805873 942582 277876 032294 607062 970275 524492 983838 967692 714027 629973 181459 599109 048470 186776 772423 692552 193582 892158 459122 074215 627500 232467 657005 307667 529164 168557 777062 119577 961342 677116 861545 633822 903324 408121 353088 522203 632414 898093 826846 191705 557615 185260 254979 213057 040555 532109 858410 284343 902557 589614 780458 725484 671974 058355 964750 790640 285310 279381 567046 502732 059255 543757 861993 499717 615078 102594 422394 958895 033196 430153 119731 686887 320829 420125 121142 744169 159076 840043 739106 889937 182603 250922 583687 819770 609658 206164 803002 942799 693322 712267 156670 473747 052944 028358 191897 883952 547719 382717 800512 417417 890622 095492 159788 604522 507487 330733 649733 465259 289941 075571 483517 655588 789029 080636 551950 125178 429642 486463 109452 872808 989147 415481 985421 848184 124599 498356 285671 793203 184764 015243 138024 435562 885025 586109 463955 418241 771969 408114 482142 969857 169665 543939 511826 233760 376603 374197 692084 911267 194017 122966 678080 906670 517055 470663 193925 985799 908347 179772 490515 492871 150639 080313 520086 308112 366952 589359 421714 120310 423970 843476 044620 957993 608418 884399 855622 999979 855617 886686 297433 212347 754269 943408 240752 501110 147760 097631 981759 582847 114029 978802 399773 466186 153078 440149 223640 669988 237234 575111 160399 317948 738887 784348 800529 719115 768576 412618 319179 219148 921780 552179 141398 403801 481182 294590 813782 629095 204318 286945 370121 131898 272305 423645 619797 048739 604114 686928 783976 915088 578168 850363 018028 255581 155745 744822 366440 801793 793983 394898 402080 705444 076768 259773 034469 288828 040087 782468 744902 571434 788827 445485 608188 565826 714084 459028 108950 321550 206515 192325 286570 742440 009522 059079 760563 205989 652868 665597 371108 589623 931515 794801 890530 085956 676099 767719 536828 600936 875608 342828 585624 234423 753986 842782 315116 140903 848148 252327 836349 077682 099506 827438 853000 820620 753052 734951 331139 275206 259014 159511 741079 913486 707588 189428 400825 228075 578603 481750 165129 582077 382168 028206 079680 181328 429010 867295 061364 415327 191554 871431 334250 707285 230540 304430 957361 678900 036501 618170 862462 482116 609909 596440 421819 328750 285868 610096 300014 209056 438676 535876 644722 577375 519310 737172 208607 878749 785861 143565 202501 418642 155016 795354 339365 779341 487481 034704 295808 267833 720861 656128 766077 391665 618857 384664 654380 164190 429436 303484 834684 111188 958351 967514 875450 687564 815939 861814 741198 230789 622623 633784 612113 328200 979090 676640 175065 933096 321818 900669 837886 053402 962466 798235 974961 210268 768272 814993 164115 147827 121176 495742 703337 747910 004842 644027 351071 414819 941584 609498 834592 976818 184497 203153 387340 473111 162203 205268 524514 127475 682836 684083 439945 567320 377022 828479 203615 350155 702537 308619 396964 455887 987105 353390 568305 123389 981163 687745 890542 005916 590364 876830 287551 855377 320020 974852 107296 767465 786279 201757 004441 613930 756159 583972 804909 855766 119822 213235 429422 777926 083464 528739 657996 864512 725100 607732 174219 689661 089342 102809 633813 017550 449823 897890 137606 655666 381104 483500 062432 470303 556839 756493 720881 510370 325630 728154 917240 667443 689490 415216 524279 672327 889497 515749 925223 770804 407684 150577 524967 896459 357964 212393 200497 925827 909587 154533 942310 237706 144735 748780 866299 131114 677508 327599 342227 937959 978019 393768 660209 402246 891640 085168 473897 395868 850651 312272 602811 010181 077852 217950 714936 046749 090774 442449 673947 / 2107 > 812131 [i]
- extracting embedded OOA [i] would yield OA(812131, 2133, S81, 2106), but