Best Known (245, 245+∞, s)-Nets in Base 4
(245, 245+∞, 258)-Net over F4 — Constructive and digital
Digital (245, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (245, 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
(245, 245+∞, 301)-Net over F4 — Digital
Digital (245, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (245, 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
(245, 245+∞, 753)-Net in Base 4 — Upper bound on s
There is no (245, m, 754)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (245, 3764, 754)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43764, 754, S4, 5, 3519), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 992139 102751 549770 246129 891792 745331 275624 743077 678937 700566 196357 258969 244958 425483 281498 304110 835907 906001 365155 301188 011002 719129 813958 263025 267660 657516 733200 538016 062333 069401 335094 550420 008890 601796 982999 500820 868148 953603 379394 101745 989022 661628 601832 169759 917928 482126 329569 952382 676504 976418 921422 062272 881893 590867 937107 400370 445189 873998 650776 885631 612269 185781 510581 869415 813141 968029 370934 005302 155213 733509 620155 514256 229923 903563 761374 530583 356704 624357 680298 277895 873276 379752 699960 085889 042911 539725 945500 288214 230821 464639 945952 264448 181557 214218 372302 051554 484190 786592 082336 540625 950969 393705 490530 721990 481412 519850 274954 305008 534971 665665 718766 111411 166845 318888 578753 763099 070475 191596 364421 379678 450648 239747 736629 213706 495166 922599 162475 478797 721997 531868 243555 303012 892079 748047 421124 606010 477813 778270 606033 308810 864925 135989 796967 556828 516334 679658 824003 987350 378100 176922 538886 638063 980206 514855 356419 391850 539284 164352 037336 069878 360775 683996 306191 408649 008307 361406 702959 972934 524649 154824 940935 613455 768135 706381 087101 006213 288929 597836 885172 041186 107410 310908 931981 861365 040934 141633 382871 883324 909244 058007 260946 904138 873697 263218 374006 272868 057970 374350 016516 878147 462918 740037 841674 948617 788624 206097 156705 380976 684417 347095 403965 725562 316269 197830 942328 898265 056594 214025 640642 769267 207893 593313 562600 370442 108827 251555 271404 028859 430532 335325 340398 554443 323815 950233 632631 988444 692050 061992 266826 392929 475681 685512 044601 511376 320763 881237 307621 893359 801150 335749 075207 898480 418437 932402 681573 328712 987090 192346 221367 039496 573947 119362 115930 038549 225559 700522 764911 073321 530151 849511 888411 285325 075370 582211 041329 734495 927931 487371 745748 602847 567469 402753 828367 636226 336097 222699 714135 055070 582467 195631 439305 222782 987806 528481 591860 252102 426892 489732 718173 815384 767732 780928 270242 229218 107683 933291 650845 173283 080845 954027 000739 163591 970606 646230 877001 479364 787236 630545 449621 268548 535213 985332 605869 992618 299248 088142 985083 506415 859743 614093 401416 616383 111208 177335 185038 123642 366795 974735 772131 565922 277325 024429 839578 133714 835053 865764 327824 870715 903071 169504 724741 123583 173920 567035 701178 633134 421786 174014 863018 083380 227254 981165 683070 251291 314205 775819 912592 838405 833145 589579 691405 696371 514933 037097 098634 871355 807182 618624 / 55 > 43764 [i]
- extracting embedded OOA [i] would yield OOA(43764, 754, S4, 5, 3519), but