Best Known (135, 160, s)-Nets in Base 4
(135, 160, 5475)-Net over F4 — Constructive and digital
Digital (135, 160, 5475)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (120, 145, 5461)-net over F4, using
- net defined by OOA [i] based on linear OOA(4145, 5461, F4, 25, 25) (dual of [(5461, 25), 136380, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4145, 65533, F4, 25) (dual of [65533, 65388, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4145, 65533, F4, 25) (dual of [65533, 65388, 26]-code), using
- net defined by OOA [i] based on linear OOA(4145, 5461, F4, 25, 25) (dual of [(5461, 25), 136380, 26]-NRT-code), using
- digital (3, 15, 14)-net over F4, using
(135, 160, 45628)-Net over F4 — Digital
Digital (135, 160, 45628)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4160, 45628, F4, 25) (dual of [45628, 45468, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4160, 65555, F4, 25) (dual of [65555, 65395, 26]-code), using
- (u, u+v)-construction [i] based on
- linear OA(415, 18, F4, 12) (dual of [18, 3, 13]-code), using
- 3 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- Simplex code S(3,4) [i]
- 3 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(415, 18, F4, 12) (dual of [18, 3, 13]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4160, 65555, F4, 25) (dual of [65555, 65395, 26]-code), using
(135, 160, large)-Net in Base 4 — Upper bound on s
There is no (135, 160, large)-net in base 4, because
- 23 times m-reduction [i] would yield (135, 137, large)-net in base 4, but