Best Known (158, 158+∞, s)-Nets in Base 4
(158, 158+∞, 130)-Net over F4 — Constructive and digital
Digital (158, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (158, 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
(158, 158+∞, 215)-Net over F4 — Digital
Digital (158, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (158, 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
(158, 158+∞, 491)-Net in Base 4 — Upper bound on s
There is no (158, m, 492)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (158, 2454, 492)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42454, 492, S4, 5, 2296), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 98124 433259 394610 654435 121143 140993 837764 698527 247728 696959 009695 937931 071523 910756 345113 567483 901991 649606 872218 654605 820666 409943 182615 853836 900881 978551 027238 765536 247416 342794 755636 478788 048263 131492 060145 201861 800297 118429 155227 865758 337497 570750 328356 120445 562539 035053 043659 100524 069771 915592 871654 556084 077366 933797 813706 716308 979138 026102 780729 040462 117383 335066 189317 797463 611282 999250 306161 975559 176747 990390 843296 062721 404644 601187 400872 879910 670620 069940 852266 629025 589598 618649 251704 044734 387468 591468 078233 058667 319375 381398 113506 874222 446148 498734 799300 869917 462051 814150 093293 070126 494787 002083 136414 448633 584364 572832 550656 984887 721095 937267 009448 921044 797347 699838 790494 926183 064643 766583 327271 720328 386971 737399 740345 834425 502512 165969 026340 815427 408579 272510 625927 659455 801210 315327 978812 307752 742939 536163 639081 190730 494050 349001 576378 075106 614899 508863 431845 989019 647874 097135 809070 061771 870803 322505 824795 524935 002325 735557 008798 420674 881900 733691 515004 265704 761353 454864 181554 149399 621367 729866 750662 272627 112282 803123 711499 662576 002102 081611 393451 234716 118303 000314 586779 141106 527048 201985 719764 107227 945596 690294 265110 209464 967291 603833 295887 001970 897244 564085 021844 212015 830646 153827 929923 398031 087180 797818 964465 743381 854279 159388 488985 229641 206000 205586 178891 914800 169726 629640 230280 903130 677684 916002 955622 436248 430023 784460 743361 013249 990098 698179 221177 015814 911768 971282 900538 072474 485951 218803 842816 952033 671557 084224 236811 636214 432312 278531 440640 / 2297 > 42454 [i]
- extracting embedded OOA [i] would yield OOA(42454, 492, S4, 5, 2296), but