Best Known (53, 53+∞, s)-Nets in Base 3
(53, 53+∞, 48)-Net over F3 — Constructive and digital
Digital (53, m, 48)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (53, 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
(53, 53+∞, 64)-Net over F3 — Digital
Digital (53, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (53, 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
(53, 53+∞, 117)-Net in Base 3 — Upper bound on s
There is no (53, m, 118)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (53, 584, 118)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3584, 118, S3, 5, 531), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 60074 732088 444453 280705 277157 101490 553823 338281 143501 150748 127312 257853 807628 492485 274420 351708 699444 017276 510796 645059 964300 976644 665433 396175 753735 044015 118064 909490 174363 739469 303649 952987 723372 252353 039260 288489 185987 352767 177915 338072 721616 793074 230635 871095 614636 978433 163978 / 133 > 3584 [i]
- extracting embedded OOA [i] would yield OOA(3584, 118, S3, 5, 531), but