Best Known (200, 236, s)-Nets in Base 4
(200, 236, 3650)-Net over F4 — Constructive and digital
Digital (200, 236, 3650)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 20, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (180, 216, 3640)-net over F4, using
- net defined by OOA [i] based on linear OOA(4216, 3640, F4, 36, 36) (dual of [(3640, 36), 130824, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(4216, 65520, F4, 36) (dual of [65520, 65304, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65535, F4, 36) (dual of [65535, 65319, 37]-code), using
- 1 times truncation [i] based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65535, F4, 36) (dual of [65535, 65319, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(4216, 65520, F4, 36) (dual of [65520, 65304, 37]-code), using
- net defined by OOA [i] based on linear OOA(4216, 3640, F4, 36, 36) (dual of [(3640, 36), 130824, 37]-NRT-code), using
- digital (2, 20, 10)-net over F4, using
(200, 236, 65384)-Net over F4 — Digital
Digital (200, 236, 65384)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 65384, F4, 36) (dual of [65384, 65148, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 65605, F4, 36) (dual of [65605, 65369, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(26) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(419, 69, F4, 8) (dual of [69, 50, 9]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,47}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,47}) [i] based on
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,47}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 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
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,3,5,47}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,47}) [i] based on
- construction X applied to Ce(36) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4236, 65605, F4, 36) (dual of [65605, 65369, 37]-code), using
(200, 236, large)-Net in Base 4 — Upper bound on s
There is no (200, 236, large)-net in base 4, because
- 34 times m-reduction [i] would yield (200, 202, large)-net in base 4, but