Best Known (202, 202+18, s)-Nets in Base 3
(202, 202+18, 932467)-Net over F3 — Constructive and digital
Digital (202, 220, 932467)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (31, 40, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- digital (162, 180, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- OA 9-folding and stacking [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]
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- digital (31, 40, 400)-net over F3, using
(202, 202+18, large)-Net over F3 — Digital
Digital (202, 220, large)-net over F3, using
- 34 times duplication [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
(202, 202+18, large)-Net in Base 3 — Upper bound on s
There is no (202, 220, large)-net in base 3, because
- 16 times m-reduction [i] would yield (202, 204, large)-net in base 3, but