Best Known (59−41, 59, s)-Nets in Base 5
(59−41, 59, 43)-Net over F5 — Constructive and digital
Digital (18, 59, 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]
(59−41, 59, 206)-Net in Base 5 — Upper bound on s
There is no (18, 59, 207)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 58, 207)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 35438 046586 626594 306835 311205 755931 482545 > 558 [i]