Best Known (154, 154+∞, s)-Nets in Base 4
(154, 154+∞, 130)-Net over F4 — Constructive and digital
Digital (154, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (154, 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
(154, 154+∞, 215)-Net over F4 — Digital
Digital (154, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (154, 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
(154, 154+∞, 479)-Net in Base 4 — Upper bound on s
There is no (154, m, 480)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (154, 2394, 480)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42394, 480, S4, 5, 2240), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2746 813725 149635 153930 727942 244022 481321 340220 970078 979378 431821 412171 229608 633773 087509 201044 730246 688618 999711 101400 306821 000742 655043 165781 945338 198670 957907 934599 262344 875408 962319 114948 374772 215358 551894 986391 617276 149945 276891 862164 966697 840418 468629 668330 238790 220507 229389 366903 255377 040811 620181 743730 906676 937685 846134 858932 187573 096257 963247 864757 564060 801975 465664 654981 337561 098978 993219 206973 573907 837331 312655 233966 403740 539654 213926 538345 382439 736537 088198 548284 472446 120481 598630 633111 116870 474195 434278 135390 121169 112787 687394 815347 942449 820471 890572 963354 217068 839706 185417 368846 668098 984713 194847 521781 049199 920901 575937 078008 915832 671393 067107 883372 613787 343440 761611 972019 896570 540152 740095 122224 082218 361290 680608 690678 942869 445513 638594 039413 601081 369557 122988 856567 606299 787410 158871 570660 825595 382187 281509 638419 234454 493764 171702 034112 072584 506453 138802 955379 912712 800867 162545 490360 940866 501099 807055 755927 430926 345955 871962 242404 082974 291912 697143 837311 431920 723473 564901 004510 509629 355557 022626 243035 191073 319242 522757 483561 183861 224743 229284 378989 770287 781850 242318 718884 574914 248280 058020 739704 646988 416262 798757 060387 014955 530506 578059 054855 298432 672021 909437 566458 336584 292121 830503 650734 598005 580711 256632 453783 848744 412616 797869 104793 283029 119846 379023 795207 956438 462969 835713 317609 890431 881328 817161 162841 979506 610925 780999 194942 920394 394789 078249 163313 958386 547414 178780 135731 870728 395921 517703 620793 991168 / 83 > 42394 [i]
- extracting embedded OOA [i] would yield OOA(42394, 480, S4, 5, 2240), but