Best Known (36, 36+50, s)-Nets in Base 27
(36, 36+50, 146)-Net over F27 — Constructive and digital
Digital (36, 86, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 29, 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 (7, 57, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 29, 64)-net over F27, using
(36, 36+50, 224)-Net in Base 27 — Constructive
(36, 86, 224)-net in base 27, using
- 6 times m-reduction [i] based on (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
- base change [i] based on digital (13, 69, 224)-net over F81, using
(36, 36+50, 244)-Net over F27 — Digital
Digital (36, 86, 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+50, 298)-Net in Base 27
(36, 86, 298)-net in base 27, using
- 10 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+50, 32837)-Net in Base 27 — Upper bound on s
There is no (36, 86, 32838)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1251 381650 148370 049013 181408 771457 319300 893569 609407 713411 935699 711371 703379 120827 694485 218354 321458 989587 385193 863688 942445 > 2786 [i]