Best Known (142, ∞, s)-Nets in Base 4
(142, ∞, 130)-Net over F4 — Constructive and digital
Digital (142, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (142, 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
(142, ∞, 176)-Net over F4 — Digital
Digital (142, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (142, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(142, ∞, 442)-Net in Base 4 — Upper bound on s
There is no (142, m, 443)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (142, 2209, 443)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42209, 443, S4, 5, 2067), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 773914 377879 049794 916765 870770 554514 203058 364841 126428 799918 415069 442319 030354 681988 615492 358244 254164 645779 531388 762792 654489 585156 194306 744211 352899 187602 844922 776108 727077 488790 094643 486571 842308 660825 598761 763076 594594 338342 318725 305268 794135 793171 514050 824400 931320 875981 703030 628461 675079 335438 874467 105282 874134 345612 346246 903140 126077 187382 080023 977778 232257 179497 928726 042272 387329 511135 747199 633664 987131 185510 781133 961671 811709 177684 345411 163512 367478 714170 201490 981473 112485 525218 754515 530091 865449 356284 470112 077288 021011 760114 367560 435626 803537 534840 049775 932742 958216 726552 802062 967767 552428 115460 847003 620120 355240 844791 997146 289255 211450 296591 327372 275133 630164 790863 810810 079566 035794 916832 392519 550826 015986 582839 958483 582991 134773 318303 565157 000859 546277 347448 730103 530721 510158 928547 061542 325045 643983 763928 820171 608437 672630 112849 732356 241982 401879 924400 176939 481509 203919 879174 809357 800135 369536 847834 916106 576129 761305 578252 907915 598978 249305 234430 433464 998367 707655 046634 877594 701602 271390 153785 591971 811244 616886 468668 477203 038681 284230 835745 095054 396505 925215 778698 673566 266034 299279 301011 765946 856115 301743 272383 585921 639954 653797 594781 312716 754259 779687 507827 862935 976443 313074 440040 133473 967071 305411 198867 065869 129501 516240 354856 366363 884832 874114 256603 804754 087238 628724 744048 473467 925499 309237 207040 / 517 > 42209 [i]
- extracting embedded OOA [i] would yield OOA(42209, 443, S4, 5, 2067), but