Best Known (44−28, 44, s)-Nets in Base 5
(44−28, 44, 37)-Net over F5 — Constructive and digital
Digital (16, 44, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 5 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(44−28, 44, 40)-Net over F5 — Digital
Digital (16, 44, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(44−28, 44, 227)-Net in Base 5 — Upper bound on s
There is no (16, 44, 228)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 5 710248 638528 115528 367967 493825 > 544 [i]