Best Known (152−14, 152, s)-Nets in Base 4
(152−14, 152, 1199738)-Net over F4 — Constructive and digital
Digital (138, 152, 1199738)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (24, 31, 1367)-net over F4, using
- net defined by OOA [i] based on linear OOA(431, 1367, F4, 7, 7) (dual of [(1367, 7), 9538, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(431, 4102, F4, 7) (dual of [4102, 4071, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(425, 4096, F4, 6) (dual of [4096, 4071, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(431, 4102, F4, 7) (dual of [4102, 4071, 8]-code), using
- net defined by OOA [i] based on linear OOA(431, 1367, F4, 7, 7) (dual of [(1367, 7), 9538, 8]-NRT-code), using
- digital (107, 121, 1198371)-net over F4, using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- digital (24, 31, 1367)-net over F4, using
(152−14, 152, large)-Net over F4 — Digital
Digital (138, 152, large)-net over F4, using
- 47 times duplication [i] based on digital (131, 145, large)-net over F4, using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
(152−14, 152, large)-Net in Base 4 — Upper bound on s
There is no (138, 152, large)-net in base 4, because
- 12 times m-reduction [i] would yield (138, 140, large)-net in base 4, but