Best Known (148−21, 148, s)-Nets in Base 4
(148−21, 148, 26224)-Net over F4 — Constructive and digital
Digital (127, 148, 26224)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 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 (115, 136, 26214)-net over F4, using
- net defined by OOA [i] based on linear OOA(4136, 26214, F4, 21, 21) (dual of [(26214, 21), 550358, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4136, 262141, F4, 21) (dual of [262141, 262005, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4136, 262141, F4, 21) (dual of [262141, 262005, 22]-code), using
- net defined by OOA [i] based on linear OOA(4136, 26214, F4, 21, 21) (dual of [(26214, 21), 550358, 22]-NRT-code), using
- digital (2, 12, 10)-net over F4, using
(148−21, 148, 131096)-Net over F4 — Digital
Digital (127, 148, 131096)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4148, 131096, F4, 2, 21) (dual of [(131096, 2), 262044, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4146, 131095, F4, 2, 21) (dual of [(131095, 2), 262044, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4146, 262190, F4, 21) (dual of [262190, 262044, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(410, 46, F4, 5) (dual of [46, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(4146, 262190, F4, 21) (dual of [262190, 262044, 22]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4146, 131095, F4, 2, 21) (dual of [(131095, 2), 262044, 22]-NRT-code), using
(148−21, 148, large)-Net in Base 4 — Upper bound on s
There is no (127, 148, large)-net in base 4, because
- 19 times m-reduction [i] would yield (127, 129, large)-net in base 4, but