Best Known (127, 127+∞, s)-Nets in Base 5
(127, 127+∞, 108)-Net over F5 — Constructive and digital
Digital (127, m, 108)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (127, 107)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 107)-sequence over F25, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- base reduction for sequences [i] based on digital (10, 107)-sequence over F25, using
(127, 127+∞, 210)-Net over F5 — Digital
Digital (127, m, 210)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (127, 209)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 127 and N(F) ≥ 210, using
(127, 127+∞, 527)-Net in Base 5 — Upper bound on s
There is no (127, m, 528)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (127, 2107, 528)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52107, 528, S5, 4, 1980), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 323171 261238 482902 994800 101226 756853 704308 191008 948269 013776 582234 298156 975201 341027 652270 989700 063769 663210 351219 030999 827547 333158 252481 828136 286935 364485 381420 957701 919876 387237 729341 067461 650482 220290 283345 718898 294516 641638 752806 880153 893827 324539 796298 642577 801747 495120 285756 461974 546442 388285 406934 779470 827635 510541 786225 041190 840872 816159 771671 980207 886599 139349 071915 223428 963699 462942 178929 294121 677342 993426 050341 163197 906139 377118 501760 361101 880647 546582 456696 762684 704108 700042 903423 362174 347584 746700 499265 389682 017216 418550 639876 788542 694757 427027 421914 558779 753365 443014 281533 060625 123993 368328 796594 402213 227627 714457 816556 955532 016010 756990 494639 759380 633421 392191 264514 381476 025551 243289 558680 827317 504091 857020 406606 597481 858052 362677 053211 558137 785220 196269 557105 682249 042151 383410 406521 759603 738835 844435 970195 608375 633032 672407 711967 857078 097335 452922 645025 681335 352535 251391 492773 111362 003038 461099 989063 133013 063800 088205 250653 059795 372443 620071 191852 300191 295715 417850 410957 417370 399899 384319 130584 506201 760033 722573 833907 091273 575053 519531 785672 173907 894624 493541 562319 033420 062327 890145 706890 616856 498105 379382 126537 429440 997133 839527 809182 180913 839647 868846 634681 925721 688811 997419 474075 403945 330199 432885 540301 427177 648089 340305 969138 634144 791565 747320 197474 093859 286094 614548 201600 531601 349351 005346 252239 185885 243218 282309 330306 345893 653382 178924 556013 520302 511067 014138 925338 607747 569834 373817 137846 036928 738868 709842 790849 506855 010986 328125 / 1981 > 52107 [i]
- extracting embedded OOA [i] would yield OOA(52107, 528, S5, 4, 1980), but