Best Known (150, ∞, s)-Nets in Base 4
(150, ∞, 130)-Net over F4 — Constructive and digital
Digital (150, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (150, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(150, ∞, 215)-Net over F4 — Digital
Digital (150, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (150, 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
(150, ∞, 467)-Net in Base 4 — Upper bound on s
There is no (150, m, 468)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (150, 2334, 468)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42334, 468, S4, 5, 2184), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 56053 079329 469660 966276 874382 299337 565022 026333 437139 837716 178730 109305 463461 282831 979275 565913 035288 331906 475947 198055 661937 085764 342709 915144 597858 504772 592406 269937 333913 901876 518103 657559 134367 024228 850447 642809 941233 953333 477770 858740 786967 690276 578623 448224 111830 135888 038332 127632 579607 152543 851093 510921 668093 224875 700090 428042 986533 844113 926179 649554 782283 470570 776301 354913 793523 198389 113637 620057 968730 657422 857807 461119 980827 085661 502599 402055 120769 798320 264293 891875 763749 183056 255828 946524 644226 033610 133492 355334 254852 943275 052986 235363 259556 881898 775791 601762 580025 846551 803126 068475 779226 460253 988600 150165 463884 373122 637312 578884 414553 278763 200207 012952 544738 917649 905734 187993 525047 240770 489051 959143 381792 171564 150607 723257 648512 117404 631899 387602 302183 416650 054214 636913 497102 822151 444208 551327 515898 153426 510478 938932 882834 842980 844009 525429 636962 393031 315721 094112 101886 508733 552429 864178 320163 837489 330840 067012 053384 519739 602970 998713 230999 447108 383526 961506 833569 401182 249031 638500 110070 668082 608710 894516 196754 197342 901082 999379 202283 854720 008542 802061 568109 290143 986745 150981 915511 340643 877307 995548 277351 293544 509515 470770 801004 206756 897297 750533 428744 660785 966891 830578 787336 688696 224978 931221 335840 699578 796917 727895 841006 323759 226779 508201 156807 783307 464612 782879 338908 015790 448192 719624 482220 681078 159725 673076 278713 240131 039075 612948 654731 927432 150111 804249 152111 834176 684032 / 2185 > 42334 [i]
- extracting embedded OOA [i] would yield OOA(42334, 468, S4, 5, 2184), but