Best Known (130, ∞, s)-Nets in Base 4
(130, ∞, 130)-Net over F4 — Constructive and digital
Digital (130, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (130, 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
(130, ∞, 176)-Net over F4 — Digital
Digital (130, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (130, 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
(130, ∞, 406)-Net in Base 4 — Upper bound on s
There is no (130, m, 407)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (130, 2029, 407)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42029, 407, S4, 5, 1899), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 078307 145467 968152 517237 223080 859756 996653 029014 556260 772863 298757 593975 680508 916034 553353 268870 212241 261063 801351 253541 285414 651384 159162 891556 261655 557344 188995 434412 970531 747042 659129 903382 265155 066475 873182 156020 798739 156994 531668 777462 387839 040350 641611 665467 739392 597194 313002 107030 530110 378560 937048 524485 800423 782780 537139 405038 297753 009719 457723 820369 969891 918860 788015 749628 912918 122936 030364 246294 110687 606066 043878 656891 005615 882365 723535 519936 570947 240061 665553 134939 679070 580501 193165 154412 578963 023545 489953 275534 651572 756894 681829 118818 288108 964099 908783 699633 108412 200547 000238 001928 060647 443837 340768 945921 974042 436614 814334 126720 191453 388345 682982 314120 830606 661437 382470 213701 588855 188294 641630 612229 550585 529239 821373 581110 782061 000760 100052 272283 746968 595615 548278 075958 774119 553612 329890 446301 493586 410561 940546 035697 397896 791643 815220 657256 049457 952689 929547 569366 624170 232272 427547 949005 730067 797810 856218 249971 989284 984848 471001 069337 411340 152129 646467 759484 445804 663313 067866 603130 795110 694618 815059 751801 704974 531972 971059 948822 039858 879238 430367 139925 793212 201753 104407 032697 956889 629996 626629 156068 051364 725473 007683 503852 563960 071784 700822 829073 329270 091886 380387 832507 783203 405282 115183 443968 / 475 > 42029 [i]
- extracting embedded OOA [i] would yield OOA(42029, 407, S4, 5, 1899), but