Best Known (63, 63+∞, s)-Nets in Base 3
(63, 63+∞, 48)-Net over F3 — Constructive and digital
Digital (63, m, 48)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 47)-sequence over F3, using
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
(63, 63+∞, 64)-Net over F3 — Digital
Digital (63, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 63)-sequence over F3, using
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
(63, 63+∞, 138)-Net in Base 3 — Upper bound on s
There is no (63, m, 139)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (63, 689, 139)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3689, 139, S3, 5, 626), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 082979 849924 461734 743859 050953 523847 564465 770513 577505 982527 033062 681397 020466 656584 933754 996978 204864 285309 582593 355472 720628 062099 966504 662793 142772 006477 816820 658510 105376 832834 777935 923642 990406 043655 139844 308843 014677 356596 854694 685846 895994 082002 209931 323233 697890 016519 680787 922888 974732 105077 698457 223710 615406 523703 762485 / 209 > 3689 [i]
- extracting embedded OOA [i] would yield OOA(3689, 139, S3, 5, 626), but