Best Known (90, 90+8, s)-Nets in Base 3
(90, 90+8, 2391490)-Net over F3 — Constructive and digital
Digital (90, 98, 2391490)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (23, 27, 1594322)-net over F3, using
- digital (63, 71, 1195745)-net over F3, using
- net defined by OOA [i] based on linear OOA(371, 1195745, F3, 8, 8) (dual of [(1195745, 8), 9565889, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(371, 4782980, F3, 8) (dual of [4782980, 4782909, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(371, 4782980, F3, 8) (dual of [4782980, 4782909, 9]-code), using
- net defined by OOA [i] based on linear OOA(371, 1195745, F3, 8, 8) (dual of [(1195745, 8), 9565889, 9]-NRT-code), using
(90, 90+8, large)-Net over F3 — Digital
Digital (90, 98, large)-net over F3, using
- 312 times duplication [i] based on digital (78, 86, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(386, large, F3, 8) (dual of [large, large−86, 9]-code), using
- 10 times code embedding in larger space [i] based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 10 times code embedding in larger space [i] based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(386, large, F3, 8) (dual of [large, large−86, 9]-code), using
(90, 90+8, large)-Net in Base 3 — Upper bound on s
There is no (90, 98, large)-net in base 3, because
- 6 times m-reduction [i] would yield (90, 92, large)-net in base 3, but