Best Known (63, 63+∞, s)-Nets in Base 5
(63, 63+∞, 82)-Net over F5 — Constructive and digital
Digital (63, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 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
(63, 63+∞, 120)-Net over F5 — Digital
Digital (63, m, 120)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 119)-sequence over F5, using
- t-expansion [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
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
(63, 63+∞, 269)-Net in Base 5 — Upper bound on s
There is no (63, m, 270)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (63, 1075, 270)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51075, 270, S5, 4, 1012), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30261 520807 776350 830814 838563 178559 057359 912910 127391 821067 123053 166374 820300 286051 749614 977150 204533 262539 587596 050211 019257 723509 301312 529424 956255 660390 035235 918682 906573 527330 556301 530750 153850 934016 458491 172256 786812 891228 810655 855293 722888 995582 981638 927326 942567 355632 040232 112142 459225 382836 597064 551456 173069 025777 081647 884978 912888 919959 213344 569058 157944 737471 943334 351306 175514 503627 141375 306977 152015 284760 508364 957445 756715 997725 161186 965392 156033 386682 909889 424114 181290 098645 608565 845222 432504 368149 320475 290084 737604 846448 574766 643418 017963 976005 302554 393232 268519 266497 873626 909643 587985 082651 020208 894670 876094 680467 457996 387606 909271 274412 104504 012118 293836 196960 889630 759928 652177 960361 951210 462028 161174 430351 820774 376392 364501 953125 / 1013 > 51075 [i]
- extracting embedded OOA [i] would yield OOA(51075, 270, S5, 4, 1012), but