Best Known (129, ∞, s)-Nets in Base 5
(129, ∞, 110)-Net over F5 — Constructive and digital
Digital (129, m, 110)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (129, 109)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 109)-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, 109)-sequence over F25, using
(129, ∞, 210)-Net over F5 — Digital
Digital (129, m, 210)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (129, 209)-sequence over F5, using
- t-expansion [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
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
(129, ∞, 535)-Net in Base 5 — Upper bound on s
There is no (129, m, 536)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (129, 2139, 536)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52139, 536, S5, 4, 2010), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30682 502000 296774 855410 931882 337869 897251 255501 648883 431908 286418 285972 487624 599496 553320 691561 073780 340563 640129 186873 297547 365228 053366 010574 833484 535797 043956 525759 418331 560142 926024 823903 107588 096769 385349 747306 352857 537673 623236 301352 965221 826086 704888 548886 457311 640296 353355 285412 614091 317073 408737 409191 165310 634628 626704 806119 282100 315317 891638 781832 020676 893987 815414 854541 826202 473513 674811 505577 203176 101908 270533 987738 929390 191045 998939 674628 217644 046142 538000 587264 319082 586606 731429 608751 628881 525825 876531 934827 223770 251534 858624 980902 759426 572669 459170 613145 122241 389038 491415 737032 779613 374885 897022 149261 426024 052397 523102 236486 902419 900937 346521 861425 030959 999776 567689 322646 643470 816947 782991 758442 543089 464505 045312 216841 836396 825331 440494 242542 015856 305536 269622 993263 718232 709376 739780 191126 447462 289751 761489 309938 777320 260854 170951 269592 768002 219627 797353 661806 886438 337415 061146 379707 219776 773228 339075 902302 610338 705372 192728 331869 797166 673871 535301 546615 017889 529893 778888 871946 600027 331259 723760 151381 052011 162935 391195 423601 439161 830572 756496 826573 510045 067915 777325 316854 107031 328266 495124 839899 735646 612405 557093 312428 074512 611583 834641 934723 321986 332909 958646 246672 692457 737783 336638 413625 493374 012831 284944 534820 513233 619238 190963 427443 864538 973859 194749 256913 568591 814982 319773 313718 620414 340484 398551 746218 167473 032011 438980 075932 790952 695443 521491 914885 011536 270588 869339 530328 083556 162315 463059 852151 559612 174254 538445 421214 287733 846504 124812 781810 760498 046875 / 2011 > 52139 [i]
- extracting embedded OOA [i] would yield OOA(52139, 536, S5, 4, 2010), but