Best Known (61, 61+88, s)-Nets in Base 3
(61, 61+88, 48)-Net over F3 — Constructive and digital
Digital (61, 149, 48)-net over F3, using
- t-expansion [i] based on digital (45, 149, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(61, 61+88, 64)-Net over F3 — Digital
Digital (61, 149, 64)-net over F3, using
- t-expansion [i] based on digital (49, 149, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(61, 61+88, 295)-Net in Base 3 — Upper bound on s
There is no (61, 149, 296)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3149, 296, S3, 88), but
- 4 times code embedding in larger space [i] would yield OA(3153, 300, S3, 88), but
- the linear programming bound shows that M ≥ 507867 127096 521475 880184 997404 262695 192753 130967 048468 307099 645865 616231 705352 414973 293091 544170 632640 665994 918879 602396 584267 068710 578966 025665 253103 480429 071113 204603 821237 163110 119107 306169 347050 081015 066703 015902 790004 687907 021927 211132 055052 585874 503800 275902 011343 796185 696370 183324 308349 875894 056099 981299 116195 082778 873527 048662 645174 336277 485509 770508 800443 298200 546236 922767 411312 994089 884498 543886 912749 984684 684759 078579 784036 839444 332090 858635 683633 842051 419090 959963 851982 915809 936015 777604 934058 220389 547175 963687 455776 525405 079802 161543 048439 330162 465703 144425 827635 921854 218168 509274 821671 908782 238324 660515 775153 717610 064197 957160 091277 908086 165280 171885 184758 570061 777311 513308 777283 615649 977056 734184 040697 020742 585835 884428 886516 897507 871358 951229 217947 246169 192386 944757 373765 404047 702645 364974 703425 562927 150613 613638 590832 060449 883146 614752 953977 145134 832500 157094 660954 924507 457896 977409 616338 878679 728474 077026 573507 120237 652744 046955 994008 830592 712650 506828 899846 134579 522619 096496 896253 226783 155191 873479 706450 791790 595074 352015 626171 319912 693431 326285 004029 896258 731213 517652 056119 661970 838491 229898 305843 241165 105326 062481 834258 587869 838452 899642 580457 197348 784320 513350 543991 508364 384067 521532 826416 443229 479644 746486 133538 439754 661987 049698 224277 971666 840120 639939 078701 662761 240183 867073 342233 722269 145054 562638 930019 666711 312384 763171 359101 584636 306861 545775 693533 724286 164097 147767 453535 259203 976524 881120 805422 981839 302570 063895 341635 530667 132163 / 32523 368500 277677 277674 373211 532352 683152 861533 392814 034304 577024 560542 545014 912844 823280 249102 114022 401625 753815 349569 203335 077291 573041 330905 603218 356205 607246 860708 473269 927558 873497 884970 546534 383974 858023 516328 472942 278254 770207 159862 212142 823964 867938 351299 261162 135527 891417 475135 607922 014086 755037 618475 919055 517224 743875 911569 279181 080709 833627 973623 543125 678192 220909 107625 696695 398600 622644 167262 979395 993401 676056 239640 128414 533817 611939 768847 614257 094740 743326 464455 421505 302384 869307 652539 558862 219345 552043 078190 125785 431070 572706 119192 909151 537132 705305 655122 301124 098060 826214 055064 162503 424701 465307 240471 262502 429251 903199 615257 409159 177430 709551 689056 271806 245294 919759 938953 917376 970815 150244 106025 067286 182060 562605 600694 173605 780044 075491 907964 802124 411197 024942 160372 677526 176278 136932 962637 358647 284875 110744 122179 484892 170245 598931 375823 254481 747332 070730 564055 387840 102666 724041 396409 142121 805828 733871 213869 498796 645953 627291 929918 770532 996153 836933 737987 055291 150052 402905 026686 374116 731654 679766 929888 324781 808155 673855 384859 497611 210330 151379 768463 596203 210938 821964 984192 160330 956320 378792 580015 666573 630747 901120 521661 525424 346516 300959 209385 809473 113822 103254 582783 535539 292986 696105 778592 015340 715051 354555 871649 524714 460597 567654 324703 146831 892811 807894 541189 469772 195482 577055 257940 686131 707680 725743 327220 640361 829602 381992 068952 475742 683599 027969 268531 495948 567715 919992 > 3153 [i]
- 4 times code embedding in larger space [i] would yield OA(3153, 300, S3, 88), but