Best Known (183, 216, s)-Nets in Base 4
(183, 216, 4117)-Net over F4 — Constructive and digital
Digital (183, 216, 4117)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (160, 193, 4096)-net over F4, using
- net defined by OOA [i] based on linear OOA(4193, 4096, F4, 33, 33) (dual of [(4096, 33), 134975, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using
- net defined by OOA [i] based on linear OOA(4193, 4096, F4, 33, 33) (dual of [(4096, 33), 134975, 34]-NRT-code), using
- digital (7, 23, 21)-net over F4, using
(183, 216, 61989)-Net over F4 — Digital
Digital (183, 216, 61989)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4216, 61989, F4, 33) (dual of [61989, 61773, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65615, F4, 33) (dual of [65615, 65399, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4215, 65614, F4, 33) (dual of [65614, 65399, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(422, 78, F4, 9) (dual of [78, 56, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4215, 65614, F4, 33) (dual of [65614, 65399, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65615, F4, 33) (dual of [65615, 65399, 34]-code), using
(183, 216, large)-Net in Base 4 — Upper bound on s
There is no (183, 216, large)-net in base 4, because
- 31 times m-reduction [i] would yield (183, 185, large)-net in base 4, but