Best Known (23, ∞, s)-Nets in Base 5
(23, ∞, 51)-Net over F5 — Constructive and digital
Digital (23, m, 51)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 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
(23, ∞, 55)-Net over F5 — Digital
Digital (23, m, 55)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
(23, ∞, 106)-Net in Base 5 — Upper bound on s
There is no (23, m, 107)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (23, 317, 107)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5317, 107, S5, 3, 294), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 093785 261150 183033 555352 858282 506414 744525 095936 822575 567153 232691 654362 972638 121248 364122 810458 435254 768317 784411 305265 979808 570744 031256 721763 093208 355049 206395 425324 306427 925804 240108 842435 574842 966161 668300 628662 109375 / 59 > 5317 [i]
- extracting embedded OOA [i] would yield OOA(5317, 107, S5, 3, 294), but