Best Known (89−18, 89, s)-Nets in Base 25
(89−18, 89, 932067)-Net over F25 — Constructive and digital
Digital (71, 89, 932067)-net over F25, using
- 253 times duplication [i] based on 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
(89−18, 89, large)-Net over F25 — Digital
Digital (71, 89, large)-net over F25, using
- 252 times duplication [i] based on digital (69, 87, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2587, large, F25, 18) (dual of [large, large−87, 19]-code), using
- 1 times code embedding in larger space [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]
- 1 times code embedding in larger space [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2587, large, F25, 18) (dual of [large, large−87, 19]-code), using
(89−18, 89, large)-Net in Base 25 — Upper bound on s
There is no (71, 89, large)-net in base 25, because
- 16 times m-reduction [i] would yield (71, 73, large)-net in base 25, but