Best Known (61, 61+∞, s)-Nets in Base 5
(61, 61+∞, 82)-Net over F5 — Constructive and digital
Digital (61, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(61, 61+∞, 120)-Net over F5 — Digital
Digital (61, m, 120)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 119)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 61 and N(F) ≥ 120, using
(61, 61+∞, 261)-Net in Base 5 — Upper bound on s
There is no (61, m, 262)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (61, 1043, 262)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51043, 262, S5, 4, 982), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 310332 400921 055654 581278 517678 031453 757634 990630 617051 474265 747001 503695 008844 839038 867808 046556 048582 374174 388804 066940 003994 078406 583420 961940 429659 596797 989135 180479 060591 765555 635495 944400 095378 462234 961505 943177 863805 173022 037302 411223 254111 579542 737328 989934 103654 542491 963634 671082 208812 656968 866682 938448 065700 778399 886775 713456 494912 791595 060950 868912 182366 471603 007250 416375 080949 158200 190182 581486 556965 001184 168289 681040 952119 514270 436347 068999 841332 499883 400596 176001 247161 829655 557674 600210 511289 863627 895715 940418 166822 226380 791878 793676 896353 759586 901585 507585 636917 084436 983397 391947 554317 185507 397070 396401 274002 009771 576139 771391 033096 710599 221485 828088 504012 927715 297229 767921 205478 842239 244841 039180 755615 234375 / 983 > 51043 [i]
- extracting embedded OOA [i] would yield OOA(51043, 262, S5, 4, 982), but