Best Known (36, 36+58, s)-Nets in Base 27
(36, 36+58, 116)-Net over F27 — Constructive and digital
Digital (36, 94, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 32, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 62, 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 (3, 32, 52)-net over F27, using
(36, 36+58, 172)-Net in Base 27 — Constructive
(36, 94, 172)-net in base 27, using
- t-expansion [i] based on (34, 94, 172)-net in base 27, using
- 14 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- 14 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
(36, 36+58, 244)-Net over F27 — Digital
Digital (36, 94, 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+58, 298)-Net in Base 27
(36, 94, 298)-net in base 27, using
- 2 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+58, 19561)-Net in Base 27 — Upper bound on s
There is no (36, 94, 19562)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 353 507720 145247 317779 809118 797010 410993 273279 867957 543012 587489 280831 374851 625797 085920 511957 599868 118960 552222 254091 120209 982854 615597 > 2794 [i]