Best Known (29, 29+9, s)-Nets in Base 27
(29, 29+9, 132899)-Net over F27 — Constructive and digital
Digital (29, 38, 132899)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (24, 33, 132861)-net over F27, using
- net defined by OOA [i] based on linear OOA(2733, 132861, F27, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(2733, 531441, F27, 9) (dual of [531441, 531408, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2733, 531445, F27, 9) (dual of [531445, 531412, 10]-code), using
- net defined by OOA [i] based on linear OOA(2733, 132861, F27, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
- digital (1, 5, 38)-net over F27, using
(29, 29+9, 911374)-Net over F27 — Digital
Digital (29, 38, 911374)-net over F27, using
(29, 29+9, large)-Net in Base 27 — Upper bound on s
There is no (29, 38, large)-net in base 27, because
- 7 times m-reduction [i] would yield (29, 31, large)-net in base 27, but