Best Known (233, ∞, s)-Nets in Base 4
(233, ∞, 258)-Net over F4 — Constructive and digital
Digital (233, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (233, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second 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) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(233, ∞, 717)-Net in Base 4 — Upper bound on s
There is no (233, m, 718)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (233, 3584, 718)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43584, 718, S4, 5, 3351), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 415995 691615 988703 699062 085593 247528 634947 579491 119483 924790 610829 741041 736895 818049 360486 631806 965406 895733 600444 737885 207853 406790 834791 876089 756698 698467 134832 543068 987337 869846 289472 264703 362401 856600 351593 439037 477845 637354 500495 889978 158831 246700 285053 999331 175944 863753 206111 407830 247022 091690 155123 519060 527309 291768 933496 174730 956099 172886 793695 278669 699393 054409 868544 339188 695794 473538 001646 338064 054743 651471 329539 408903 426429 354697 423022 537983 523031 991948 852052 502617 262946 234654 077364 647949 130051 628076 660728 508210 713851 533744 978628 605332 042417 033750 653139 738895 514039 436502 292079 172949 242280 976468 863494 935745 531548 677748 774734 885971 883487 698650 716659 780659 926088 013749 963710 898110 794344 738425 054392 161314 965044 689085 526034 941242 238156 035286 899708 489179 322635 403545 291620 642941 582912 698404 997088 318591 672297 579460 925769 314551 312690 598509 279276 465406 670556 636376 338310 508866 742907 473411 833359 556780 160113 630542 270719 506427 662565 471839 722629 621142 998657 060180 558478 168769 148922 385748 134156 357818 108992 669879 021481 854314 461150 567332 587844 729757 652784 260763 264140 469396 211708 728432 089299 951781 002585 279340 028724 578754 624035 473914 172835 077578 135309 372738 295548 828450 501447 201074 925037 364426 685793 785127 230333 145737 523781 457420 538708 279918 071792 304001 026406 023908 470080 556255 591976 593108 382371 937046 515951 336422 900754 825213 819945 181731 913242 605970 708052 723854 597137 179450 636620 439675 033631 287353 122167 884409 938236 573725 227917 728378 129600 686156 213229 333333 369231 528895 088965 193171 600046 605947 906407 750552 294260 005990 833366 601493 263748 309331 824906 995748 465180 060390 045226 076504 626148 549421 926059 307083 054931 487217 219420 072798 950563 137177 432417 966994 464295 135896 596339 849651 966581 054937 770517 451251 060381 464674 515872 950779 598532 532450 013207 611784 779278 934069 915455 012085 467015 459219 066803 438471 711783 286855 869386 159520 126192 618923 906123 519163 717190 188846 662836 652345 592722 938934 029145 228161 847929 458978 354478 585710 934041 330386 487564 258174 965755 886926 783001 258511 582912 055977 020913 190363 585150 948735 057925 390085 190850 079959 917488 950253 968957 289697 711492 019135 719431 210541 603645 180598 899235 060300 111200 044812 717846 935328 623002 561646 594163 046608 532750 204928 / 419 > 43584 [i]
- extracting embedded OOA [i] would yield OOA(43584, 718, S4, 5, 3351), but