Best Known (147, 147+23, s)-Nets in Base 4
(147, 147+23, 23849)-Net over F4 — Constructive and digital
Digital (147, 170, 23849)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 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 (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 (5, 16, 17)-net over F4, using
(147, 147+23, 202528)-Net over F4 — Digital
Digital (147, 170, 202528)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4170, 202528, F4, 23) (dual of [202528, 202358, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4170, 262208, F4, 23) (dual of [262208, 262038, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(14) [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(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(22) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4170, 262208, F4, 23) (dual of [262208, 262038, 24]-code), using
(147, 147+23, large)-Net in Base 4 — Upper bound on s
There is no (147, 170, large)-net in base 4, because
- 21 times m-reduction [i] would yield (147, 149, large)-net in base 4, but