Best Known (202, 202+15, s)-Nets in Base 4
(202, 202+15, 4815348)-Net over F4 — Constructive and digital
Digital (202, 217, 4815348)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (38, 45, 21864)-net over F4, using
- net defined by OOA [i] based on linear OOA(445, 21864, F4, 9, 7) (dual of [(21864, 9), 196731, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(445, 21865, F4, 3, 7) (dual of [(21865, 3), 65550, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(44, 17, F4, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- linear OOA(441, 21848, F4, 3, 7) (dual of [(21848, 3), 65503, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(441, 65544, F4, 7) (dual of [65544, 65503, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(441, 65536, F4, 7) (dual of [65536, 65495, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 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 [i] based on linear OA(441, 65544, F4, 7) (dual of [65544, 65503, 8]-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(445, 21865, F4, 3, 7) (dual of [(21865, 3), 65550, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(445, 21864, F4, 9, 7) (dual of [(21864, 9), 196731, 8]-NRT-code), using
- digital (157, 172, 4793484)-net over F4, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- digital (38, 45, 21864)-net over F4, using
(202, 202+15, large)-Net over F4 — Digital
Digital (202, 217, large)-net over F4, using
- t-expansion [i] based on digital (195, 217, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
(202, 202+15, large)-Net in Base 4 — Upper bound on s
There is no (202, 217, large)-net in base 4, because
- 13 times m-reduction [i] would yield (202, 204, large)-net in base 4, but