Best Known (143, 143+∞, s)-Nets in Base 4
(143, 143+∞, 130)-Net over F4 — Constructive and digital
Digital (143, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 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
(143, 143+∞, 176)-Net over F4 — Digital
Digital (143, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (143, 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
(143, 143+∞, 445)-Net in Base 4 — Upper bound on s
There is no (143, m, 446)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (143, 2224, 446)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42224, 446, S4, 5, 2081), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3410 913542 604913 494266 071896 593113 948201 065388 851022 071078 927231 209411 852893 917176 350506 461263 151648 407324 902062 700829 546570 816635 192230 060442 266205 277082 940163 915158 111950 750434 312154 048830 364275 757840 929218 262960 290327 845215 490588 004189 745421 999869 821805 409479 402358 232793 072318 300136 572524 657394 445736 052805 100893 940177 543307 573758 284491 191417 673673 051944 133359 079233 196687 283084 214587 144419 559307 441993 580397 628101 932926 632325 881506 618809 221572 286239 684756 049200 764497 381594 639384 004767 752946 011616 471236 022943 860109 452638 252699 142071 544882 101625 597264 423310 098946 205045 327181 680835 546125 067863 743170 547619 056592 965535 912032 649638 172090 710765 520413 372927 821389 475443 863792 424842 412554 177029 621106 660610 188928 513750 690865 442809 039336 574803 394924 276879 277311 661509 566262 370848 447804 317746 107903 831875 436655 478103 737915 874691 112906 117185 379307 331703 402805 037541 491389 097346 869862 431925 409976 173345 737097 031087 821698 264474 045780 344922 772671 880966 901712 411180 084943 978574 163418 537972 343083 739666 091603 209114 730266 286696 074639 256502 282255 697056 958069 915013 774255 229431 931876 380454 104155 003751 816082 056274 047191 477906 177868 086566 094471 466794 157236 287023 956129 576722 970539 545320 285373 827467 287134 509112 997310 633050 873913 778759 899137 850579 999984 699412 379859 985217 928100 971242 806636 864357 233984 517513 433812 107549 358505 817436 021458 486637 663445 057536 / 347 > 42224 [i]
- extracting embedded OOA [i] would yield OOA(42224, 446, S4, 5, 2081), but