Best Known (60−27, 60, s)-Nets in Base 3
(60−27, 60, 56)-Net over F3 — Constructive and digital
Digital (33, 60, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 30, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(60−27, 60, 402)-Net in Base 3 — Upper bound on s
There is no (33, 60, 403)-net in base 3, because
- 1 times m-reduction [i] would yield (33, 59, 403)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 14401 995855 981063 974378 416719 > 359 [i]