Best Known (169−26, 169, s)-Nets in Base 4
(169−26, 169, 5055)-Net over F4 — Constructive and digital
Digital (143, 169, 5055)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 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 (127, 153, 5041)-net over F4, using
- net defined by OOA [i] based on linear OOA(4153, 5041, F4, 26, 26) (dual of [(5041, 26), 130913, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4153, 65533, F4, 26) (dual of [65533, 65380, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4153, 65533, F4, 26) (dual of [65533, 65380, 27]-code), using
- net defined by OOA [i] based on linear OOA(4153, 5041, F4, 26, 26) (dual of [(5041, 26), 130913, 27]-NRT-code), using
- digital (3, 16, 14)-net over F4, using
(169−26, 169, 53519)-Net over F4 — Digital
Digital (143, 169, 53519)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4169, 53519, F4, 26) (dual of [53519, 53350, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, 65555, F4, 26) (dual of [65555, 65386, 27]-code), using
- (u, u+v)-construction [i] based on
- linear OA(416, 19, F4, 13) (dual of [19, 3, 14]-code), using
- 2 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- Simplex code S(3,4) [i]
- 2 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(416, 19, F4, 13) (dual of [19, 3, 14]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4169, 65555, F4, 26) (dual of [65555, 65386, 27]-code), using
(169−26, 169, large)-Net in Base 4 — Upper bound on s
There is no (143, 169, large)-net in base 4, because
- 24 times m-reduction [i] would yield (143, 145, large)-net in base 4, but