Best Known (203, 203+17, s)-Nets in Base 3
(203, 203+17, 1195750)-Net over F3 — Constructive and digital
Digital (203, 220, 1195750)-net over F3, using
- trace code for nets [i] based on digital (93, 110, 597875)-net over F9, using
- net defined by OOA [i] based on linear OOA(9110, 597875, F9, 17, 17) (dual of [(597875, 17), 10163765, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- net defined by OOA [i] based on linear OOA(9110, 597875, F9, 17, 17) (dual of [(597875, 17), 10163765, 18]-NRT-code), using
(203, 203+17, large)-Net over F3 — Digital
Digital (203, 220, large)-net over F3, using
- 34 times duplication [i] based on digital (199, 216, large)-net over F3, using
- t-expansion [i] based on digital (198, 216, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
- 36 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 36 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
- t-expansion [i] based on digital (198, 216, large)-net over F3, using
(203, 203+17, large)-Net in Base 3 — Upper bound on s
There is no (203, 220, large)-net in base 3, because
- 15 times m-reduction [i] would yield (203, 205, large)-net in base 3, but