MinT - Best Known (147−85, 147, s)-Nets in Base 3

Best Known (147−85, 147, s)-Nets in Base 3

(147−85, 147, 48)-Net over F₃ — Constructive and digital

Digital (62, 147, 48)-net over F₃, using

t-expansion [i] based on digital (45, 147, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(147−85, 147, 64)-Net over F₃ — Digital

Digital (62, 147, 64)-net over F₃, using

t-expansion [i] based on digital (49, 147, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(147−85, 147, 298)-Net in Base 3 — Upper bound on s

There is no (62, 147, 299)-net in base 3, because

1 times m-reduction [i] would yield (62, 146, 299)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁴⁶, 299, S₃, 84), but
  - 1 times code embedding in larger space [i] would yield OA(3¹⁴⁷, 300, S₃, 84), but
    - the linear programming bound shows that MÂ â‰¥ 4947 151175 729525 270705 810167 826983 636137 008791 818978 652782 822592 423973 183988 052442 749043 185730 293286 636936 943654 635818 455690 876066 448829 465776 933535 151812 888331 851887 735655 665501 181020 147482 838465 703363 276010 040902 882210 083454 475880 985715 701245 726140 530436 569419 052644 569411 581729 090777 088601 244400 147273 807904 446467 853214 443827 852075 439859 758687 738493 463745 101873 439327 913342 332910 354998 064424 050677 440110 099789 644734 794554 430802 073124 021953 797873 447190 509495 628226 672017 178600 247646 929300 338403 192072 723944 451918 259047 273468 493249 676370 724334 291410 438077 531451 388258 311771 088078 086185 351494 823008 215190 524385 590708 617925 310359 559633 153909 713217 556107 152538 076035 940063 997716 135879 314627 495959 762068 647217 096945 890357 510511 421693 142776 563191 826388 161113 344326 286625 108681 609680 955692 344826 350716 057860 427065 511318 606396 450683 958383 951923 588045 441511 654223 502047 930581 631889 666528 907639 582385 951917 922555 808141 444970 896211 307906 881831 810837 481137 582807 332648 905128 230093 565582 446982 444799 292658 239444 205537 342357 523186 118246 681863 810714 926710 079125 018868 043587 489603 873394 643498 747673 228563 563604 752282 611731 348739 595828 872629 567786 855584 625496 490979 135110 713351 859650 822474 282354 580124 739359 247380 902614 910278 005444 998604 994457 018740 423431 190341 522810 383616 959751 320122 086606 994101 096388 990713 278943 441927 080228 407285 143034 440683 503828 500419 750869 881496 873551 239027 489497 003707 902079 322494 600261 512327 590627 757592 012393 231416 243129 274966 288230 056090 279308 132277 456424 736982 673257 439000 821563 092296 776174 786885 / 311722 519270 831617 975535 218010 639538 040559 766638 460746 607959 884508 138269 628422 023673 958037 791525 775986 073077 003941 652773 586692 131241 124975 182260 262638 529189 774343 200849 477888 697036 012364 768020 231823 748350 754300 193820 285722 314614 127627 735355 686084 700698 220620 407297 613602 536724 577101 615031 846898 655579 369370 105873 588157 723770 024716 955024 461939 798169 384297 350722 206879 815274 049679 664760 362054 766360 447489 865686 822581 275409 870343 483171 557944 215456 252413 581877 855889 192896 056438 282325 795497 463772 961980 803588 428191 567229 355219 941872 713355 983284 471921 545309 155663 155535 562601 525073 412634 247926 667770 868782 380559 391897 391170 692010 906905 024529 652277 543251 820034 776357 492074 330791 920920 229354 504953 041910 409910 914422 232367 488573 433003 191867 216706 719960 955028 843231 116580 436672 055733 950044 801741 554139 044588 663870 453520 762834 980634 257355 773884 516731 149897 978228 870621 303967 690206 493874 907624 994715 564750 415152 347667 340039 201625 236376 240972 028439 302949 646729 433090 275474 580212 858148 684454 907722 204976 988509 303688 920306 333884 074555 095458 724261 164236 586575 973994 906779 759687 231669 693136 902888 786733 194415 056685 648304 912396 667485 318610 910067 766881 117532 568379 083802 079189 213180 022743 189492 005614 132836 387311 032068 708030 019300 753194 349146 266561 014251 747047 779723 909279 194042 448262 816776 466484 597397 695540 185423 320416 729873 596212 919807 884769 940586 084612 548206 529309 391907 985690 853124 622247 793490 752825 861377 483067 526634 066145 063592 533026 415683 191910 137909 > 3¹⁴⁷ [i]

Best Known (147−85, 147, s)-Nets in Base 3

(147−85, 147, 48)-Net over F3 — Constructive and digital

(147−85, 147, 64)-Net over F3 — Digital

(147−85, 147, 298)-Net in Base 3 — Upper bound on s

(147−85, 147, 48)-Net over F₃ — Constructive and digital

(147−85, 147, 64)-Net over F₃ — Digital