Best Known (213, 213+∞, s)-Nets in Base 4
(213, 213+∞, 200)-Net over F4 — Constructive and digital
Digital (213, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (213, 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
(213, 213+∞, 258)-Net over F4 — Digital
Digital (213, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (213, 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
(213, 213+∞, 656)-Net in Base 4 — Upper bound on s
There is no (213, m, 657)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (213, 3279, 657)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43279, 657, S4, 5, 3066), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4597 983792 494619 816716 014069 857917 399606 029924 119947 282446 657664 988645 870275 560539 627608 334084 923647 215038 611691 621516 790898 748777 874476 268811 543077 480759 979171 020154 375917 937470 706206 497159 718685 496374 753655 481570 538499 491142 691087 223596 950062 502856 645947 397017 509411 874407 507514 388342 058031 696333 579950 461678 532781 143273 696035 676623 482858 218119 007290 750299 735519 656666 850003 267218 820477 766056 580882 600275 843797 479712 373505 737010 221154 767011 270030 379289 801711 290641 874403 831411 960712 362941 104124 412843 140409 953746 166775 475684 911841 493984 329498 289806 172290 915936 310477 890965 965944 762688 677174 476822 656953 869283 151362 741359 232463 557412 911621 410007 779040 647692 925962 255812 698947 918741 071535 322184 737731 394769 975903 371778 910059 056613 037560 882582 022735 822463 361827 917645 239260 839303 053594 161282 874314 516533 403230 518013 719595 490658 981608 131857 716416 260582 701552 349048 572844 750475 230955 098100 379318 964866 299744 047219 855558 432918 070896 487953 170557 771676 543160 806025 046036 326556 782804 826178 881713 223749 549949 741867 286097 215058 226742 150954 040992 268156 435622 211813 702037 323668 101950 347475 599517 065910 574661 272620 066222 611721 628193 166685 051104 515844 576235 438214 934668 831762 891012 530035 114557 919499 289018 137911 818318 694921 048187 863400 345103 009844 046506 690371 926426 539855 205550 963095 479548 572618 532219 711081 395046 119476 873117 217257 823842 745180 426767 032381 607066 385219 983496 800712 182218 271529 858548 633959 635804 778615 659617 633148 094799 002724 197338 406562 379061 318842 005654 484236 442743 755339 852419 778617 864715 591081 887420 853424 149845 344685 041827 670418 891930 820309 187850 684647 756505 026320 873752 849526 426992 097566 527287 887220 070329 503336 452415 642970 861482 459498 315370 936222 312864 781125 824717 395052 484588 869828 207059 909208 408903 020713 839277 525337 574119 566389 720670 455415 428751 304170 733187 029701 027614 505680 814432 915853 845933 186519 077032 212613 130989 879812 735215 855127 045474 240034 043184 480098 387547 170071 540408 567737 297482 813453 091166 860887 585479 269670 356967 509714 179175 710314 326275 107180 835955 015680 / 3067 > 43279 [i]
- extracting embedded OOA [i] would yield OOA(43279, 657, S4, 5, 3066), but