Best Known (75−17, 75, s)-Nets in Base 27
(75−17, 75, 66478)-Net over F27 — Constructive and digital
Digital (58, 75, 66478)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (48, 65, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- digital (2, 10, 48)-net over F27, using
(75−17, 75, 1339941)-Net over F27 — Digital
Digital (58, 75, 1339941)-net over F27, using
(75−17, 75, large)-Net in Base 27 — Upper bound on s
There is no (58, 75, large)-net in base 27, because
- 15 times m-reduction [i] would yield (58, 60, large)-net in base 27, but