Best Known (72, 72+21, s)-Nets in Base 27
(72, 72+21, 53192)-Net over F27 — Constructive and digital
Digital (72, 93, 53192)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 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 (60, 81, 53144)-net over F27, using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- digital (2, 12, 48)-net over F27, using
(72, 72+21, 1446030)-Net over F27 — Digital
Digital (72, 93, 1446030)-net over F27, using
(72, 72+21, large)-Net in Base 27 — Upper bound on s
There is no (72, 93, large)-net in base 27, because
- 19 times m-reduction [i] would yield (72, 74, large)-net in base 27, but