Best Known (173, 190, s)-Nets in Base 4
(173, 190, 2097155)-Net over F4 — Constructive and digital
Digital (173, 190, 2097155)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (165, 182, 2097150)-net over F4, using
- net defined by OOA [i] based on linear OOA(4182, 2097150, F4, 18, 17) (dual of [(2097150, 18), 37748518, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4182, 8388601, F4, 2, 17) (dual of [(8388601, 2), 16777020, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4182, 8388601, F4, 2, 17) (dual of [(8388601, 2), 16777020, 18]-NRT-code), using
- net defined by OOA [i] based on linear OOA(4182, 2097150, F4, 18, 17) (dual of [(2097150, 18), 37748518, 18]-NRT-code), using
- digital (0, 8, 5)-net over F4, using
(173, 190, large)-Net over F4 — Digital
Digital (173, 190, large)-net over F4, using
- 44 times duplication [i] based on digital (169, 186, large)-net over F4, using
- t-expansion [i] based on digital (167, 186, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- t-expansion [i] based on digital (167, 186, large)-net over F4, using
(173, 190, large)-Net in Base 4 — Upper bound on s
There is no (173, 190, large)-net in base 4, because
- 15 times m-reduction [i] would yield (173, 175, large)-net in base 4, but