MinT - Best Known (52, 52+66, s)-Nets in Base 3

Best Known (52, 52+66, s)-Nets in Base 3

Digital (52, 118, 48)-net over F₃, using

Digital (52, 118, 64)-net over F₃, using

t-expansion [i] based on digital (49, 118, 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]

There is no (52, 118, 299)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹¹⁸, 299, S₃, 66), but
- 1 times code embedding in larger space [i] would yield OA(3¹¹⁹, 300, S₃, 66), but
  - the linear programming bound shows that MÂ â‰¥ 1 086339 578612 299107 648571 692666 406053 214598 540595 955078 498498 616003 636271 024005 883880 021197 383030 912590 055266 372641 117375 343006 249739 908456 432441 191550 480174 677652 585616 711654 696134 395480 373617 987256 880315 395424 420607 313547 637731 369269 186535 340656 348415 430089 999325 481184 290961 650793 385301 404352 654289 012976 382254 508438 028764 340037 582653 983452 615600 344981 556963 359506 268902 752477 350925 779343 836992 833031 489756 018638 958486 854803 533226 798132 469860 / 1585 215724 352125 837651 868417 294884 366625 425214 893470 572248 973126 061511 214094 669043 644348 258606 046042 660054 703500 796762 277780 269300 611116 671923 899504 773979 155315 584494 820832 057911 644319 335306 195943 208632 318301 606469 133835 565465 659022 625888 134621 990526 344695 376370 471385 379773 769963 838516 662637 578566 937539 455487 372723 983141 638151 114954 697576 086896 814302 039395 533515 174323 290004 648336 884099 > 3¹¹⁹ [i]