Best Known (48, 48+∞, s)-Nets in Base 3
(48, 48+∞, 48)-Net over F3 — Constructive and digital
Digital (48, m, 48)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (48, 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
(48, 48+∞, 56)-Net over F3 — Digital
Digital (48, m, 56)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (48, 55)-sequence over F3, using
- t-expansion [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- t-expansion [i] based on digital (40, 55)-sequence over F3, using
(48, 48+∞, 107)-Net in Base 3 — Upper bound on s
There is no (48, m, 108)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (48, 534, 108)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3534, 108, S3, 5, 486), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 343821 538392 794744 971988 367444 317149 888019 219654 310042 978368 480701 286267 732702 345837 301631 075869 708080 900589 987744 222222 378349 655973 124873 248600 186718 565415 389661 554907 134496 046023 218886 509206 619300 572111 944324 007291 155879 944548 899070 269532 503024 107801 974623 / 487 > 3534 [i]
- extracting embedded OOA [i] would yield OOA(3534, 108, S3, 5, 486), but