Best Known (29, ∞, s)-Nets in Base 5
(29, ∞, 51)-Net over F5 — Constructive and digital
Digital (29, m, 51)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 50)-sequence over F5, using
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
(29, ∞, 56)-Net over F5 — Digital
Digital (29, m, 56)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 55)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 29 and N(F) ≥ 56, using
(29, ∞, 131)-Net in Base 5 — Upper bound on s
There is no (29, m, 132)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (29, 392, 132)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5392, 132, S5, 3, 363), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 140091 059731 639299 517628 218439 501983 924672 530139 164030 799597 409931 796172 879958 748055 573649 771153 097329 732140 514224 035243 590774 235863 347932 889770 434112 346384 845517 177615 644268 326194 392097 062647 604334 277835 116335 042613 365935 863248 428502 707276 788186 163685 168139 636516 571044 921875 / 91 > 5392 [i]
- extracting embedded OOA [i] would yield OOA(5392, 132, S5, 3, 363), but