Best Known (79, 97, s)-Nets in Base 25
(79, 97, 932095)-Net over F25 — Constructive and digital
Digital (79, 97, 932095)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (68, 86, 932067)-net over F25, using
- net defined by OOA [i] based on linear OOA(2586, 932067, F25, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2586, 932067, F25, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (2, 11, 28)-net over F25, using
(79, 97, large)-Net over F25 — Digital
Digital (79, 97, large)-net over F25, using
- t-expansion [i] based on digital (77, 97, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2597, large, F25, 20) (dual of [large, large−97, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2597, large, F25, 20) (dual of [large, large−97, 21]-code), using
(79, 97, large)-Net in Base 25 — Upper bound on s
There is no (79, 97, large)-net in base 25, because
- 16 times m-reduction [i] would yield (79, 81, large)-net in base 25, but