Best Known (246, 246+∞, s)-Nets in Base 4
(246, 246+∞, 258)-Net over F4 — Constructive and digital
Digital (246, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (246, 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
(246, 246+∞, 301)-Net over F4 — Digital
Digital (246, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (246, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(246, 246+∞, 756)-Net in Base 4 — Upper bound on s
There is no (246, m, 757)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (246, 3779, 757)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43779, 757, S4, 5, 3533), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11353 012960 701299 419678 254157 331605 478818 803307 890049 556046 209387 776861 296199 089973 950152 589743 994049 971596 509261 979326 542709 534446 634044 526906 893529 777861 692953 129079 339086 509432 887684 513948 626020 994181 896489 063656 787740 609444 046990 315039 469963 945486 426238 685070 381612 978313 469420 051165 942842 608400 017899 022932 301537 325663 736830 324602 935494 285810 578986 892128 528316 674792 523737 966787 960586 613787 328148 979972 223730 890648 383832 599757 968080 471337 171488 732972 324052 730383 660918 493878 273674 679480 301921 684136 064281 756676 402168 829446 495914 362763 001056 028352 134670 700107 081562 757021 313752 052748 504960 949953 646830 192368 160956 276968 636374 082696 345695 709329 071100 518846 786764 313236 022147 487627 773484 800635 716337 378164 228379 400230 420650 776889 298528 242264 479400 466995 516264 569786 369525 224397 780191 373192 072331 697236 277897 457067 102579 298690 656490 759647 859840 068854 444817 520573 505250 844297 976882 825599 709357 098933 266197 073615 304302 825812 895444 674506 464776 150532 365800 814822 936581 078641 836534 765750 908572 242113 364160 115103 956605 960251 269637 871830 679326 716624 793887 568825 342902 746464 612006 405984 836980 652089 143392 219447 780316 314330 294674 688640 557638 798868 006629 879851 064742 917195 456711 263637 136924 741458 376614 226973 769209 205062 788859 608175 908455 469465 234358 604535 778612 001349 348875 201175 570320 333825 331095 756173 257105 476157 558885 784839 054853 094637 402582 859048 856826 269099 500338 298015 446282 167441 855975 434970 676105 730997 411306 497458 635060 957907 106127 465721 362922 139862 846134 019992 306622 855365 651634 019151 336975 089056 999998 846265 471165 828322 391127 600108 786060 659073 523851 878683 659580 078768 703492 478456 499690 320504 317039 182207 353891 312009 705802 236755 929782 393092 180471 080556 542840 736431 250238 630627 615267 891004 756883 741197 972884 332046 759792 354215 288475 819967 549588 821985 223251 837634 829326 200105 982122 618103 906822 012889 283556 011083 713850 928081 046721 184548 818226 999366 418784 941308 608390 144887 564809 593013 359637 066320 618355 426255 630908 608988 472093 940812 757994 590320 772461 966989 349255 147802 896810 918178 611112 388278 053281 187873 268122 159017 491633 692103 639429 053561 268665 343289 544391 488980 863602 181040 535986 506362 530886 872359 086473 386754 144242 488111 008701 156840 973113 354641 205424 944331 336482 863010 535371 347284 681108 228866 002648 012531 711004 211373 494249 285970 313650 906644 566603 636042 976741 111452 194515 714048 / 589 > 43779 [i]
- extracting embedded OOA [i] would yield OOA(43779, 757, S4, 5, 3533), but