Best Known (57−22, 57, s)-Nets in Base 27
(57−22, 57, 228)-Net over F27 — Constructive and digital
Digital (35, 57, 228)-net over F27, using
- 1 times m-reduction [i] based on digital (35, 58, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 12, 76)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 730)-net over F27, using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- digital (1, 8, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (1, 4, 730)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 29, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (5, 12, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(57−22, 57, 370)-Net in Base 27 — Constructive
(35, 57, 370)-net in base 27, using
- 19 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
(57−22, 57, 2573)-Net over F27 — Digital
Digital (35, 57, 2573)-net over F27, using
(57−22, 57, 4932954)-Net in Base 27 — Upper bound on s
There is no (35, 57, 4932955)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3870 214647 822151 584857 860909 666472 843738 180394 746371 658097 415578 859383 707944 583379 > 2757 [i]