Best Known (65−44, 65, s)-Nets in Base 5
(65−44, 65, 43)-Net over F5 — Constructive and digital
Digital (21, 65, 43)-net over F5, using
- t-expansion [i] based on digital (18, 65, 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
(65−44, 65, 50)-Net over F5 — Digital
Digital (21, 65, 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
(65−44, 65, 247)-Net in Base 5 — Upper bound on s
There is no (21, 65, 248)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2867 589412 544504 070334 134997 144436 484408 859521 > 565 [i]