Best Known (60, 60+∞, s)-Nets in Base 5
(60, 60+∞, 82)-Net over F5 — Constructive and digital
Digital (60, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (60, 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
(60, 60+∞, 112)-Net over F5 — Digital
Digital (60, m, 112)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (60, 111)-sequence over F5, using
- t-expansion [i] based on digital (57, 111)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 57 and N(F) ≥ 112, using
- t-expansion [i] based on digital (57, 111)-sequence over F5, using
(60, 60+∞, 257)-Net in Base 5 — Upper bound on s
There is no (60, m, 258)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (60, 1027, 258)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51027, 258, S5, 4, 967), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 077770 150214 425669 934331 472457 883218 606182 740536 441980 424267 967554 739648 112991 626116 918405 146685 025585 720117 682220 470955 620710 297002 457240 227130 999167 332553 985220 590617 063628 826061 165167 501448 722337 008069 612775 246257 181762 109471 392443 795740 786487 915297 286575 454742 495518 310526 053923 731143 867505 722631 765609 281246 196537 146805 532134 302781 226869 937655 543056 178338 417931 433834 904930 389438 978322 916998 395780 556870 199560 731921 366495 550055 746955 967248 601947 241673 352894 157118 669953 684495 121357 865472 674275 562988 371702 294568 522665 115792 953201 094846 493471 104167 887231 837909 677186 859343 765721 028103 452008 856614 948385 288725 423484 441479 826187 395580 603413 270362 091131 905587 347351 478590 224359 808968 923601 923961 541615 426540 374755 859375 / 121 > 51027 [i]
- extracting embedded OOA [i] would yield OOA(51027, 258, S5, 4, 967), but