Best Known (40−28, 40, s)-Nets in Base 4
(40−28, 40, 28)-Net over F4 — Constructive and digital
Digital (12, 40, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
(40−28, 40, 29)-Net over F4 — Digital
Digital (12, 40, 29)-net over F4, using
- net from sequence [i] based on digital (12, 28)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 29, using
(40−28, 40, 95)-Net in Base 4 — Upper bound on s
There is no (12, 40, 96)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 366123 673729 854645 470901 > 440 [i]
- extracting embedded orthogonal array [i] would yield OA(440, 96, S4, 28), but
- the linear programming bound shows that M ≥ 3 041221 052768 594873 805769 980859 249005 438281 138205 879215 063040 / 2 375396 786313 270370 198219 858144 081283 > 440 [i]