Best Known (154, 176, s)-Nets in Base 4
(154, 176, 95341)-Net over F4 — Constructive and digital
Digital (154, 176, 95341)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 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 (139, 161, 95326)-net over F4, using
- net defined by OOA [i] based on linear OOA(4161, 95326, F4, 22, 22) (dual of [(95326, 22), 2097011, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4161, 1048586, F4, 22) (dual of [1048586, 1048425, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 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(21) ⊂ Ce(20) [i] based on
- OA 11-folding and stacking [i] based on linear OA(4161, 1048586, F4, 22) (dual of [1048586, 1048425, 23]-code), using
- net defined by OOA [i] based on linear OOA(4161, 95326, F4, 22, 22) (dual of [(95326, 22), 2097011, 23]-NRT-code), using
- digital (4, 15, 15)-net over F4, using
(154, 176, 524325)-Net over F4 — Digital
Digital (154, 176, 524325)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4176, 524325, F4, 2, 22) (dual of [(524325, 2), 1048474, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4176, 1048650, F4, 22) (dual of [1048650, 1048474, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4176, 1048651, F4, 22) (dual of [1048651, 1048475, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4176, 1048651, F4, 22) (dual of [1048651, 1048475, 23]-code), using
- OOA 2-folding [i] based on linear OA(4176, 1048650, F4, 22) (dual of [1048650, 1048474, 23]-code), using
(154, 176, large)-Net in Base 4 — Upper bound on s
There is no (154, 176, large)-net in base 4, because
- 20 times m-reduction [i] would yield (154, 156, large)-net in base 4, but