Best Known (23, 23+26, s)-Nets in Base 27
(23, 23+26, 140)-Net over F27 — Constructive and digital
Digital (23, 49, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 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 (6, 32, 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 (4, 17, 64)-net over F27, using
(23, 23+26, 172)-Net in Base 27 — Constructive
(23, 49, 172)-net in base 27, using
- 15 times m-reduction [i] based on (23, 64, 172)-net in base 27, using
- base change [i] based on digital (7, 48, 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, 48, 172)-net over F81, using
(23, 23+26, 263)-Net over F27 — Digital
Digital (23, 49, 263)-net over F27, using
(23, 23+26, 54140)-Net in Base 27 — Upper bound on s
There is no (23, 49, 54141)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13705 425314 052723 582529 456791 488933 326120 027678 665677 964842 074156 678467 > 2749 [i]