MinT - Best Known (145−98, 145, s)-Nets in Base 4

Best Known (145−98, 145, s)-Nets in Base 4

(145−98, 145, 56)-Net over F₄ — Constructive and digital

Digital (47, 145, 56)-net over F₄, using

t-expansion [i] based on digital (33, 145, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(145−98, 145, 81)-Net over F₄ — Digital

Digital (47, 145, 81)-net over F₄, using

t-expansion [i] based on digital (46, 145, 81)-net over F₄, using
- net from sequence [i] based on digital (46, 80)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(145−98, 145, 297)-Net in Base 4 — Upper bound on s

There is no (47, 145, 298)-net in base 4, because

1 times m-reduction [i] would yield (47, 144, 298)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(4¹⁴⁴, 298, S₄, 97), but
  - 2 times code embedding in larger space [i] would yield OA(4¹⁴⁶, 300, S₄, 97), but
    - the linear programming bound shows that MÂ â‰¥ 20 716311 762681 600759 020024 155708 201101 421775 247420 785248 329609 362232 077927 243791 966483 540948 450415 091775 350715 889978 522032 005783 684362 203031 829651 840439 803840 593259 929534 164228 999031 608854 613293 214852 824556 185455 002921 205963 036092 863438 610112 310018 276953 074152 080181 360689 225972 292729 713351 566743 139302 232488 209338 528798 021526 045445 192198 621123 075431 669228 651061 296655 030900 415768 929499 441433 613274 629795 637539 208356 417809 349641 264882 073377 027521 626474 855792 227710 342921 444351 119933 228547 331971 370579 422245 841112 743958 738228 278370 445148 423134 861012 293391 295077 981905 798707 192015 145258 470810 249016 888856 166235 477330 438979 567596 377435 432520 808878 023571 437882 344396 129260 052263 563891 956841 246064 671743 710440 635961 862080 368412 489098 545427 913210 396647 707653 613887 884359 368070 438709 717784 829928 682477 758964 504225 896844 424569 492081 704390 682329 028186 960201 291834 463395 540887 719109 697252 483949 130837 944166 961258 639209 974739 199642 477675 386541 874761 916356 305912 594694 734282 508813 552899 114213 164413 755232 494534 266923 809809 788095 599978 490439 168334 493542 255372 509690 674514 273110 595310 109449 018192 836772 852458 600113 022263 514587 367448 312988 742921 374166 429537 431018 917000 696936 049313 442559 495418 576746 558457 332565 093637 581409 697863 654097 228336 984989 106176 / 1587 175349 653582 347518 597544 330537 328951 865924 748197 079348 630505 632676 376909 406342 226629 189780 063514 478170 410298 732297 055896 696786 864890 631691 307515 214561 508310 726125 624650 616801 924964 555346 650933 410690 245805 355341 399551 478755 906566 550380 298543 217315 897294 998205 408703 850831 231159 027056 408227 164225 968960 346451 782078 333427 354854 986119 224301 841637 474531 278885 570171 193626 373600 043231 793689 440973 286449 942090 030106 987796 123777 887307 791556 818821 988943 449464 132918 717414 558764 750008 353130 131186 807710 437687 235014 797929 419419 752623 466477 499472 575001 824028 517791 075228 267493 609010 685368 130702 700737 876378 108144 920807 366818 122544 392966 227350 235465 878061 221628 501445 212777 576206 551326 248594 506009 315251 196220 022312 454848 908819 157224 982775 875545 473782 116249 552071 726940 004089 313926 574218 862490 350065 612881 269506 189126 156813 588559 468534 647941 652453 292900 129693 226755 428582 961243 826939 402484 804047 397729 845045 941944 681505 077622 375761 665227 849494 570498 913195 715396 249828 595921 156649 946480 142857 191406 333490 865561 100223 461268 783917 493921 547248 092132 548209 842165 272329 348005 098210 974193 084896 646874 563101 744681 106816 556655 588083 945275 850027 491473 929449 970265 333311 > 4¹⁴⁶ [i]

Best Known (145−98, 145, s)-Nets in Base 4

(145−98, 145, 56)-Net over F4 — Constructive and digital

(145−98, 145, 81)-Net over F4 — Digital

(145−98, 145, 297)-Net in Base 4 — Upper bound on s

(145−98, 145, 56)-Net over F₄ — Constructive and digital

(145−98, 145, 81)-Net over F₄ — Digital