Best Known (46, 46+∞, s)-Nets in Base 5
(46, 46+∞, 78)-Net over F5 — Constructive and digital
Digital (46, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 77)-sequence over F5, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
(46, 46+∞, 88)-Net over F5 — Digital
Digital (46, m, 88)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 87)-sequence over F5, using
- t-expansion [i] based on digital (45, 87)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 45 and N(F) ≥ 88, using
- t-expansion [i] based on digital (45, 87)-sequence over F5, using
(46, 46+∞, 201)-Net in Base 5 — Upper bound on s
There is no (46, m, 202)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (46, 602, 202)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5602, 202, S5, 3, 556), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4126 987768 988689 051631 034434 445171 553638 095984 598200 276759 388710 884451 598023 197026 677104 736053 398322 623330 112613 091427 584086 323711 800695 020829 545180 782546 083731 227034 011034 414876 745043 229480 723449 298171 835636 487425 904230 714655 567429 475624 938144 783250 683673 733911 413749 884042 797988 017831 692044 679561 709446 028620 138336 413665 258877 313228 608016 683937 450114 330068 624096 615547 815535 693311 657372 550627 087548 491545 021533 966064 453125 / 557 > 5602 [i]
- extracting embedded OOA [i] would yield OOA(5602, 202, S5, 3, 556), but