Best Known (190, 224, s)-Nets in Base 4
(190, 224, 3872)-Net over F4 — Constructive and digital
Digital (190, 224, 3872)-net over F4, using
- 41 times duplication [i] based on digital (189, 223, 3872)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 22, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (167, 201, 3855)-net over F4, using
- net defined by OOA [i] based on linear OOA(4201, 3855, F4, 34, 34) (dual of [(3855, 34), 130869, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(4201, 65535, F4, 34) (dual of [65535, 65334, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(4201, 65535, F4, 34) (dual of [65535, 65334, 35]-code), using
- net defined by OOA [i] based on linear OOA(4201, 3855, F4, 34, 34) (dual of [(3855, 34), 130869, 35]-NRT-code), using
- digital (5, 22, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(190, 224, 65621)-Net over F4 — Digital
Digital (190, 224, 65621)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4224, 65621, F4, 34) (dual of [65621, 65397, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(22) [i] based on
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(423, 85, F4, 10) (dual of [85, 62, 11]-code), using
- a “GraCyc†code from Grassl’s database [i]
- construction X applied to Ce(33) ⊂ Ce(22) [i] based on
(190, 224, large)-Net in Base 4 — Upper bound on s
There is no (190, 224, large)-net in base 4, because
- 32 times m-reduction [i] would yield (190, 192, large)-net in base 4, but