Best Known (18, 18+18, s)-Nets in Base 3
(18, 18+18, 28)-Net over F3 — Constructive and digital
Digital (18, 36, 28)-net over F3, using
- t-expansion [i] based on digital (15, 36, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(18, 18+18, 29)-Net over F3 — Digital
Digital (18, 36, 29)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(336, 29, F3, 3, 18) (dual of [(29, 3), 51, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(333, 28, F3, 3, 18) (dual of [(28, 3), 51, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,65P) [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(333, 28, F3, 3, 18) (dual of [(28, 3), 51, 19]-NRT-code), using
(18, 18+18, 159)-Net in Base 3 — Upper bound on s
There is no (18, 36, 160)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 153046 304772 197185 > 336 [i]