Best Known (72, 72+20, s)-Nets in Base 27
(72, 72+20, 53212)-Net over F27 — Constructive and digital
Digital (72, 92, 53212)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (57, 77, 53144)-net over F27, using
- net defined by OOA [i] based on linear OOA(2777, 53144, F27, 20, 20) (dual of [(53144, 20), 1062803, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2777, 531440, F27, 20) (dual of [531440, 531363, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2777, 531440, F27, 20) (dual of [531440, 531363, 21]-code), using
- net defined by OOA [i] based on linear OOA(2777, 53144, F27, 20, 20) (dual of [(53144, 20), 1062803, 21]-NRT-code), using
- digital (5, 15, 68)-net over F27, using
(72, 72+20, 53244)-Net in Base 27 — Constructive
(72, 92, 53244)-net in base 27, using
- base change [i] based on digital (49, 69, 53244)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (38, 58, 53144)-net over F81, using
- net defined by OOA [i] based on linear OOA(8158, 53144, F81, 20, 20) (dual of [(53144, 20), 1062822, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8158, 531440, F81, 20) (dual of [531440, 531382, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8158, 531440, F81, 20) (dual of [531440, 531382, 21]-code), using
- net defined by OOA [i] based on linear OOA(8158, 53144, F81, 20, 20) (dual of [(53144, 20), 1062822, 21]-NRT-code), using
- digital (1, 11, 100)-net over F81, using
- (u, u+v)-construction [i] based on
(72, 72+20, 2600505)-Net over F27 — Digital
Digital (72, 92, 2600505)-net over F27, using
(72, 72+20, large)-Net in Base 27 — Upper bound on s
There is no (72, 92, large)-net in base 27, because
- 18 times m-reduction [i] would yield (72, 74, large)-net in base 27, but