Best Known (162, 162+∞, s)-Nets in Base 4
(162, 162+∞, 200)-Net over F4 — Constructive and digital
Digital (162, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (162, 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
(162, 162+∞, 215)-Net over F4 — Digital
Digital (162, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (162, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(162, 162+∞, 503)-Net in Base 4 — Upper bound on s
There is no (162, m, 504)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (162, 2514, 504)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42514, 504, S4, 5, 2352), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 129823 093787 944136 844947 700828 340417 823345 887567 513744 435717 069553 484881 101230 567733 352744 892566 663402 451840 772322 113200 220239 339493 483577 755425 074862 171739 960322 660305 873670 568901 438939 796421 519780 792098 926321 779194 372363 038516 002316 401937 626449 782205 101975 207233 002922 827061 654177 080600 618965 430959 052474 007044 922957 873541 491703 148562 044926 700838 511963 190994 380029 035071 514648 305430 736664 129938 990746 158254 051637 555310 447010 413892 145613 532173 814999 964604 615987 895178 443256 169814 252699 544917 835094 639879 120164 862118 715153 916035 400411 028475 291052 093138 208533 325730 457268 840898 034321 655033 554978 813557 881643 193031 252545 436577 447854 252565 135463 788780 049051 404951 371045 910231 927348 367531 938544 735413 180686 818982 079888 477279 102626 884937 755261 085133 055342 971444 312534 775249 110535 416465 752721 350204 508914 354183 706744 834389 199803 542749 143424 120418 558923 967090 440730 863835 196966 694320 954355 236530 056541 103612 843544 537150 557645 003575 570760 308443 539597 809481 322235 169326 467601 435538 361318 019551 912256 662790 000647 466913 388903 620421 882922 936355 947707 744927 664416 271870 827627 960813 272602 873041 191211 212518 758506 196091 582391 549004 166138 979435 442661 748301 203516 073031 921468 287048 445805 204390 730612 333911 825268 496813 646994 503986 779871 241388 222067 893373 475160 055629 187157 882254 797108 810303 286574 894313 221379 301817 557278 229545 237419 679250 685861 998636 189343 060394 754955 591127 744289 606056 293959 052307 867581 352071 292403 493409 254735 940020 852844 241155 693384 871496 964252 368020 077680 152728 651910 023277 457378 096139 076456 026125 437514 103174 201344 / 2353 > 42514 [i]
- extracting embedded OOA [i] would yield OOA(42514, 504, S4, 5, 2352), but