Best Known (21, 21+∞, s)-Nets in Base 5
(21, 21+∞, 43)-Net over F5 — Constructive and digital
Digital (21, m, 43)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (21, 42)-sequence over F5, using
- t-expansion [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (18, 42)-sequence over F5, using
(21, 21+∞, 50)-Net over F5 — Digital
Digital (21, m, 50)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(21, 21+∞, 98)-Net in Base 5 — Upper bound on s
There is no (21, m, 99)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (21, 293, 99)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5293, 99, S5, 3, 272), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 722 618558 091825 348615 697631 773979 774645 951723 439918 975984 420030 049941 893495 036574 070926 408530 295263 375201 421734 387412 517138 317619 454518 622493 266182 108839 420171 657124 368491 675880 932234 576903 283596 038818 359375 / 91 > 5293 [i]
- extracting embedded OOA [i] would yield OOA(5293, 99, S5, 3, 272), but