Best Known (223−21, 223, s)-Nets in Base 3
(223−21, 223, 838870)-Net over F3 — Constructive and digital
Digital (202, 223, 838870)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-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 (3, 13, 10)-net over F3, using
(223−21, 223, 2796211)-Net over F3 — Digital
Digital (202, 223, 2796211)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 2796211, F3, 3, 21) (dual of [(2796211, 3), 8388410, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(313, 10, F3, 3, 10) (dual of [(10, 3), 17, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,19P) [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, 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(313, 10, F3, 3, 10) (dual of [(10, 3), 17, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(223−21, 223, large)-Net in Base 3 — Upper bound on s
There is no (202, 223, large)-net in base 3, because
- 19 times m-reduction [i] would yield (202, 204, large)-net in base 3, but