Best Known (49−28, 49, s)-Nets in Base 5
(49−28, 49, 43)-Net over F5 — Constructive and digital
Digital (21, 49, 43)-net over F5, using
- t-expansion [i] based on digital (18, 49, 43)-net over F5, using
- net from sequence [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]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(49−28, 49, 50)-Net over F5 — Digital
Digital (21, 49, 50)-net over F5, 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
(49−28, 49, 412)-Net in Base 5 — Upper bound on s
There is no (21, 49, 413)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 18028 820662 693993 079016 199094 590825 > 549 [i]