Best Known (243−23, 243, s)-Nets in Base 3
(243−23, 243, 762614)-Net over F3 — Constructive and digital
Digital (220, 243, 762614)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- digital (203, 226, 762600)-net over F3, using
- net defined by OOA [i] based on linear OOA(3226, 762600, F3, 23, 23) (dual of [(762600, 23), 17539574, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3226, 8388601, F3, 23) (dual of [8388601, 8388375, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3226, 8388601, F3, 23) (dual of [8388601, 8388375, 24]-code), using
- net defined by OOA [i] based on linear OOA(3226, 762600, F3, 23, 23) (dual of [(762600, 23), 17539574, 24]-NRT-code), using
- digital (6, 17, 14)-net over F3, using
(243−23, 243, 2796215)-Net over F3 — Digital
Digital (220, 243, 2796215)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 2796215, F3, 3, 23) (dual of [(2796215, 3), 8388402, 24]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(317, 14, F3, 3, 11) (dual of [(14, 3), 25, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,30P) [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- linear OOA(3226, 2796201, F3, 3, 23) (dual of [(2796201, 3), 8388377, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- OOA 3-folding [i] based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- linear OOA(317, 14, F3, 3, 11) (dual of [(14, 3), 25, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(243−23, 243, large)-Net in Base 3 — Upper bound on s
There is no (220, 243, large)-net in base 3, because
- 21 times m-reduction [i] would yield (220, 222, large)-net in base 3, but