Best Known (173, ∞, s)-Nets in Base 4
(173, ∞, 200)-Net over F4 — Constructive and digital
Digital (173, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (173, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(173, ∞, 215)-Net over F4 — Digital
Digital (173, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (173, 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
(173, ∞, 536)-Net in Base 4 — Upper bound on s
There is no (173, m, 537)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (173, 2679, 537)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42679, 537, S4, 5, 2506), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 280 306693 112335 765896 110503 618864 667924 952992 811407 116641 697653 877141 207900 990173 215026 414413 003819 255557 159776 104060 262926 296130 204193 091314 258942 429056 286282 863174 127019 061775 734272 092215 707452 513734 514075 482765 894885 646681 919347 085124 430702 382086 414137 515472 957067 184223 699964 634264 723857 786787 224349 409535 072733 697526 439384 425815 336995 772774 070734 976852 528913 462107 504791 949456 427997 566787 642987 910143 950510 445834 042103 484260 558600 247525 471210 586108 329817 468339 081998 041489 723854 901894 713751 230596 174786 067017 133551 737506 060312 346094 211280 039981 704064 333715 332345 485924 679367 874605 397920 585846 365628 868350 940157 645406 971009 374636 876329 862468 322931 453357 949868 490344 455702 131819 112513 973261 754459 365360 920066 738089 608781 963025 262877 784017 660081 214894 452457 185180 600568 786820 088534 053769 480121 139869 642852 925400 349221 703680 667551 685235 448678 056669 094002 522214 304383 383967 820273 362632 754638 788089 022185 386667 285292 010996 565844 489074 416276 240157 754916 922595 665356 757000 231632 885009 943172 981130 788474 127080 293189 799622 065737 526235 443286 652645 365386 538046 136354 325870 734587 564706 406666 272679 189353 271759 799742 016941 583040 387577 847926 283581 640434 061717 815651 666525 719784 069321 120018 284406 633098 777774 262330 670484 659446 566041 337030 055481 914547 112607 236117 137582 624770 738341 412028 274400 206371 806242 555666 539145 691999 652503 443025 515719 902986 568751 666185 869666 320391 815604 708724 087844 042924 232376 054706 864908 899812 156754 141810 922676 167539 684052 427593 912177 671076 302008 272619 020619 710695 921415 150856 365753 606565 319654 823839 791195 031460 369763 500452 464384 604901 708701 016197 921656 175630 747370 823615 564388 018222 093795 412641 054720 / 2507 > 42679 [i]
- extracting embedded OOA [i] would yield OOA(42679, 537, S4, 5, 2506), but