Best Known (159, ∞, s)-Nets in Base 4
(159, ∞, 130)-Net over F4 — Constructive and digital
Digital (159, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (159, 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
(159, ∞, 215)-Net over F4 — Digital
Digital (159, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (159, 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
(159, ∞, 494)-Net in Base 4 — Upper bound on s
There is no (159, m, 495)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (159, 2469, 495)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42469, 495, S4, 5, 2310), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 105 237795 960923 856898 025950 665122 876770 891745 819597 256085 452084 847028 974755 920260 303974 092487 744943 047691 603649 938226 852206 302108 177799 144546 511093 035997 831529 668071 806921 431219 503106 162915 913636 232557 799724 598917 651063 300850 577455 771067 310664 698491 248825 423958 177515 987772 627695 668954 144599 016482 703463 279607 737223 311271 254499 002084 256967 000489 488271 764272 569568 880546 993846 333148 116375 156643 159638 540254 218125 542882 188749 020410 683431 404346 690072 015833 796175 246763 321961 891530 267076 909088 895146 164260 594184 285820 182685 107227 785999 368201 734544 315789 431398 900034 026357 692318 373695 034787 840927 821594 224549 653062 431368 648298 697063 160968 181280 296225 440808 035819 198486 825941 450359 349492 575959 612659 651499 712707 250898 802873 922125 896585 557683 371625 364693 569925 565505 892702 026855 965841 428903 528361 934313 393783 823474 617546 539753 871011 262662 045574 122053 675700 974458 048838 202215 228202 986256 028982 620834 818914 768420 810317 122034 343102 722603 328703 264501 824169 446636 929382 589041 692609 685073 869847 807441 785909 446969 639365 787477 117467 391117 779418 723482 883210 306828 875293 635473 894977 737866 074599 360510 085387 919965 752992 371693 317400 989862 432207 826823 254008 629340 191389 620922 164666 357244 042620 681106 380431 681230 738821 165286 155905 523379 330119 054756 421517 271552 092206 811691 923436 799067 791223 448677 155062 094559 551301 181391 039132 308841 612427 661110 585004 599548 847379 908814 467420 184807 640486 478163 312678 404234 771525 238691 860133 810170 470221 263779 902981 351073 538803 742923 896647 139082 666507 313060 972382 452494 015171 395584 / 2311 > 42469 [i]
- extracting embedded OOA [i] would yield OOA(42469, 495, S4, 5, 2310), but