Best Known (226−22, 226, s)-Nets in Base 3
(226−22, 226, 762612)-Net over F3 — Constructive and digital
Digital (204, 226, 762612)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 12)-net over F3, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- digital (189, 211, 762600)-net over F3, using
- net defined by OOA [i] based on linear OOA(3211, 762600, F3, 22, 22) (dual of [(762600, 22), 16776989, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3211, 8388600, F3, 22) (dual of [8388600, 8388389, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3211, 8388600, F3, 22) (dual of [8388600, 8388389, 23]-code), using
- net defined by OOA [i] based on linear OOA(3211, 762600, F3, 22, 22) (dual of [(762600, 22), 16776989, 23]-NRT-code), using
- digital (4, 15, 12)-net over F3, using
(226−22, 226, 2796213)-Net over F3 — Digital
Digital (204, 226, 2796213)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3226, 2796213, F3, 3, 22) (dual of [(2796213, 3), 8388413, 23]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(315, 12, F3, 3, 11) (dual of [(12, 3), 21, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,24P) [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
- linear OOA(3211, 2796201, F3, 3, 22) (dual of [(2796201, 3), 8388392, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 3-folding [i] based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- linear OOA(315, 12, F3, 3, 11) (dual of [(12, 3), 21, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(226−22, 226, large)-Net in Base 3 — Upper bound on s
There is no (204, 226, large)-net in base 3, because
- 20 times m-reduction [i] would yield (204, 206, large)-net in base 3, but