Best Known (24, 48, s)-Nets in Base 27
(24, 48, 152)-Net over F27 — Constructive and digital
Digital (24, 48, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 18, 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, 30, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 18, 76)-net over F27, using
(24, 48, 172)-Net in Base 27 — Constructive
(24, 48, 172)-net in base 27, using
- 20 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(24, 48, 388)-Net over F27 — Digital
Digital (24, 48, 388)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2748, 388, F27, 24) (dual of [388, 340, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2748, 728, F27, 24) (dual of [728, 680, 25]-code), using
(24, 48, 108098)-Net in Base 27 — Upper bound on s
There is no (24, 48, 108099)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 507 563901 426176 225947 095647 568314 659311 665951 350720 588279 885187 125289 > 2748 [i]