Best Known (145, 168, s)-Nets in Base 4
(145, 168, 23846)-Net over F4 — Constructive and digital
Digital (145, 168, 23846)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 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 (131, 154, 23832)-net over F4, using
- net defined by OOA [i] based on linear OOA(4154, 23832, F4, 23, 23) (dual of [(23832, 23), 547982, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4154, 262153, F4, 23) (dual of [262153, 261999, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(4154, 262153, F4, 23) (dual of [262153, 261999, 24]-code), using
- net defined by OOA [i] based on linear OOA(4154, 23832, F4, 23, 23) (dual of [(23832, 23), 547982, 24]-NRT-code), using
- digital (3, 14, 14)-net over F4, using
(145, 168, 177477)-Net over F4 — Digital
Digital (145, 168, 177477)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4168, 177477, F4, 23) (dual of [177477, 177309, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4168, 262186, F4, 23) (dual of [262186, 262018, 24]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4168, 262186, F4, 23) (dual of [262186, 262018, 24]-code), using
(145, 168, large)-Net in Base 4 — Upper bound on s
There is no (145, 168, large)-net in base 4, because
- 21 times m-reduction [i] would yield (145, 147, large)-net in base 4, but