Best Known (222−21, 222, s)-Nets in Base 3
(222−21, 222, 838868)-Net over F3 — Constructive and digital
Digital (201, 222, 838868)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (189, 210, 838860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3210, 838860, F3, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3210, 8388601, F3, 21) (dual of [8388601, 8388391, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3210, 8388601, F3, 21) (dual of [8388601, 8388391, 22]-code), using
- net defined by OOA [i] based on linear OOA(3210, 838860, F3, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
- digital (2, 12, 8)-net over F3, using
(222−21, 222, 2796209)-Net over F3 — Digital
Digital (201, 222, 2796209)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3222, 2796209, F3, 3, 21) (dual of [(2796209, 3), 8388405, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(312, 8, F3, 3, 10) (dual of [(8, 3), 12, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,13P) [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- linear OOA(3210, 2796201, F3, 3, 21) (dual of [(2796201, 3), 8388393, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- OOA 3-folding [i] based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- linear OOA(312, 8, F3, 3, 10) (dual of [(8, 3), 12, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(222−21, 222, large)-Net in Base 3 — Upper bound on s
There is no (201, 222, large)-net in base 3, because
- 19 times m-reduction [i] would yield (201, 203, large)-net in base 3, but