Best Known (11, 11+20, s)-Nets in Base 3
(11, 11+20, 20)-Net over F3 — Constructive and digital
Digital (11, 31, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
(11, 11+20, 59)-Net in Base 3 — Upper bound on s
There is no (11, 31, 60)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 688 780623 580041 > 331 [i]