Best Known (62−6, 62, s)-Nets in Base 4
(62−6, 62, 5592402)-Net over F4 — Constructive and digital
Digital (56, 62, 5592402)-net over F4, using
- trace code for nets [i] based on digital (25, 31, 2796201)-net over F16, using
- net defined by OOA [i] based on linear OOA(1631, 2796201, F16, 6, 6) (dual of [(2796201, 6), 16777175, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(1631, large, F16, 6) (dual of [large, large−31, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(1631, large, F16, 6) (dual of [large, large−31, 7]-code), using
- net defined by OOA [i] based on linear OOA(1631, 2796201, F16, 6, 6) (dual of [(2796201, 6), 16777175, 7]-NRT-code), using
(62−6, 62, large)-Net over F4 — Digital
Digital (56, 62, large)-net over F4, using
- 41 times duplication [i] based on digital (55, 61, large)-net over F4, using
- t-expansion [i] based on digital (54, 61, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- t-expansion [i] based on digital (54, 61, large)-net over F4, using
(62−6, 62, large)-Net in Base 4 — Upper bound on s
There is no (56, 62, large)-net in base 4, because
- 4 times m-reduction [i] would yield (56, 58, large)-net in base 4, but