Best Known (93−20, 93, s)-Nets in Base 27
(93−20, 93, 53220)-Net over F27 — Constructive and digital
Digital (73, 93, 53220)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-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 (6, 16, 76)-net over F27, using
(93−20, 93, 53260)-Net in Base 27 — Constructive
(73, 93, 53260)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, 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
- (6, 16, 116)-net in base 27, using
(93−20, 93, 3093089)-Net over F27 — Digital
Digital (73, 93, 3093089)-net over F27, using
(93−20, 93, large)-Net in Base 27 — Upper bound on s
There is no (73, 93, large)-net in base 27, because
- 18 times m-reduction [i] would yield (73, 75, large)-net in base 27, but