Best Known (76, 76+29, s)-Nets in Base 9
(76, 76+29, 756)-Net over F9 — Constructive and digital
Digital (76, 105, 756)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (61, 90, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 45, 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
- trace code for nets [i] based on digital (16, 45, 370)-net over F81, using
- digital (1, 15, 16)-net over F9, using
(76, 76+29, 6454)-Net over F9 — Digital
Digital (76, 105, 6454)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9105, 6454, F9, 29) (dual of [6454, 6349, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(9105, 6562, F9, 29) (dual of [6562, 6457, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9105, 6562, F9, 29) (dual of [6562, 6457, 30]-code), using
(76, 76+29, large)-Net in Base 9 — Upper bound on s
There is no (76, 105, large)-net in base 9, because
- 27 times m-reduction [i] would yield (76, 78, large)-net in base 9, but