Best Known (219, ∞, s)-Nets in Base 4
(219, ∞, 200)-Net over F4 — Constructive and digital
Digital (219, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (219, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(219, ∞, 258)-Net over F4 — Digital
Digital (219, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (219, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
(219, ∞, 674)-Net in Base 4 — Upper bound on s
There is no (219, m, 675)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (219, 3369, 675)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43369, 675, S4, 5, 3150), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6993 869984 494826 075375 230144 701521 367386 203784 209025 973447 097374 656896 042691 688429 873525 135904 272501 050525 148793 122852 782826 333219 296893 008742 029652 987718 835792 414825 561563 668192 541983 146181 783531 704370 127294 756789 439362 559180 611312 775691 305367 623427 366417 899277 527687 862570 174250 559504 063776 376331 844004 060829 399482 891573 543220 224820 052071 904237 681890 667177 091899 204079 194947 933119 325883 851031 074493 642800 933532 432479 231292 594550 394333 148431 043287 801238 393378 894972 975937 009221 438973 264331 103108 223108 439846 427958 258663 412735 959284 882525 157310 429076 780342 393047 318560 366304 362711 391555 929639 915294 283376 390033 958099 587069 692051 422249 299445 025412 090750 147192 908103 400042 562863 089613 630873 657849 031679 798220 214391 048691 807933 475752 725636 340807 014002 328289 433889 545344 677064 090473 626680 260488 319381 662460 152666 813129 676982 852645 634688 172093 178769 066501 907205 823547 135533 557784 191043 470107 250790 687744 218130 150778 776132 587040 606499 090443 522437 074696 369102 027305 481150 266493 582542 382983 003120 792472 877219 390494 720539 873485 282491 542627 625442 447802 698822 400334 748169 505580 851920 351507 280473 649949 704295 739043 745419 226176 055941 270367 689457 126398 963286 960365 413386 109939 415949 825729 387199 299372 950525 501495 528626 658530 801398 497066 308720 254843 919486 833011 036544 933982 825183 968922 237312 150978 508175 173020 391550 024996 456489 565134 301058 742625 925233 215117 711850 030859 788246 814749 001647 239535 870953 147059 053800 800857 914406 774272 844224 037054 319564 854404 083607 262051 111372 490725 145602 681444 107555 387240 682017 992719 279928 282621 032009 380011 173982 041040 279509 610885 462376 436363 423645 496822 076006 770113 762006 256474 631534 265543 702295 062900 350589 095407 069664 114360 333101 214110 811353 552883 856115 984616 222520 834520 895902 103819 531803 383119 629200 901304 941868 516109 977755 143146 031384 321165 281073 893042 230627 700945 441001 630721 394573 577083 158160 116955 044250 413474 492600 899125 523723 439271 812281 986035 425707 470569 156319 074576 920655 706199 005826 505851 307785 480049 523545 573661 941555 573534 153706 301518 432353 864431 923034 067442 028735 609217 851625 477331 091890 718872 961024 / 3151 > 43369 [i]
- extracting embedded OOA [i] would yield OOA(43369, 675, S4, 5, 3150), but