Best Known (33, 33+10, s)-Nets in Base 27
(33, 33+10, 106327)-Net over F27 — Constructive and digital
Digital (33, 43, 106327)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (27, 37, 106289)-net over F27, using
- net defined by OOA [i] based on linear OOA(2737, 106289, F27, 10, 10) (dual of [(106289, 10), 1062853, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2737, 531445, F27, 10) (dual of [531445, 531408, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(2737, 531441, F27, 10) (dual of [531441, 531404, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(8) [i] based on
- OA 5-folding and stacking [i] based on linear OA(2737, 531445, F27, 10) (dual of [531445, 531408, 11]-code), using
- net defined by OOA [i] based on linear OOA(2737, 106289, F27, 10, 10) (dual of [(106289, 10), 1062853, 11]-NRT-code), using
- digital (1, 6, 38)-net over F27, using
(33, 33+10, 1100317)-Net over F27 — Digital
Digital (33, 43, 1100317)-net over F27, using
(33, 33+10, large)-Net in Base 27 — Upper bound on s
There is no (33, 43, large)-net in base 27, because
- 8 times m-reduction [i] would yield (33, 35, large)-net in base 27, but