Best Known (159, 180, s)-Nets in Base 4
(159, 180, 419445)-Net over F4 — Constructive and digital
Digital (159, 180, 419445)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (145, 166, 419430)-net over F4, using
- net defined by OOA [i] based on linear OOA(4166, 419430, F4, 21, 21) (dual of [(419430, 21), 8807864, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4166, 4194301, F4, 21) (dual of [4194301, 4194135, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4166, 4194301, F4, 21) (dual of [4194301, 4194135, 22]-code), using
- net defined by OOA [i] based on linear OOA(4166, 419430, F4, 21, 21) (dual of [(419430, 21), 8807864, 22]-NRT-code), using
- digital (4, 14, 15)-net over F4, using
(159, 180, 2097186)-Net over F4 — Digital
Digital (159, 180, 2097186)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4180, 2097186, F4, 2, 21) (dual of [(2097186, 2), 4194192, 22]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4179, 2097186, F4, 2, 21) (dual of [(2097186, 2), 4194193, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4179, 4194372, F4, 21) (dual of [4194372, 4194193, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(413, 68, F4, 6) (dual of [68, 55, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 70, F4, 6) (dual of [70, 57, 7]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(4179, 4194372, F4, 21) (dual of [4194372, 4194193, 22]-code), using
- 41 times duplication [i] based on linear OOA(4179, 2097186, F4, 2, 21) (dual of [(2097186, 2), 4194193, 22]-NRT-code), using
(159, 180, large)-Net in Base 4 — Upper bound on s
There is no (159, 180, large)-net in base 4, because
- 19 times m-reduction [i] would yield (159, 161, large)-net in base 4, but