Best Known (36, 36+56, s)-Nets in Base 27
(36, 36+56, 128)-Net over F27 — Constructive and digital
Digital (36, 92, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 32, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 60, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 32, 64)-net over F27, using
(36, 36+56, 224)-Net in Base 27 — Constructive
(36, 92, 224)-net in base 27, using
- base change [i] based on digital (13, 69, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(36, 36+56, 244)-Net over F27 — Digital
Digital (36, 92, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
(36, 36+56, 298)-Net in Base 27
(36, 92, 298)-net in base 27, using
- 4 times m-reduction [i] based on (36, 96, 298)-net in base 27, using
- base change [i] based on digital (12, 72, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 72, 298)-net over F81, using
(36, 36+56, 21917)-Net in Base 27 — Upper bound on s
There is no (36, 92, 21918)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 484866 555146 423056 668169 662114 907570 059000 676251 377982 066351 955601 002291 567538 781969 354728 540106 264794 277600 964724 565255 384313 120889 > 2792 [i]