Best Known (72, 88, s)-Nets in Base 27
(72, 88, 1048639)-Net over F27 — Constructive and digital
Digital (72, 88, 1048639)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (60, 76, 1048575)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (4, 12, 64)-net over F27, using
(72, 88, 1048675)-Net in Base 27 — Constructive
(72, 88, 1048675)-net in base 27, using
- (u, u+v)-construction [i] based on
- (4, 12, 100)-net in base 27, using
- base change [i] based on digital (1, 9, 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
- base change [i] based on digital (1, 9, 100)-net over F81, using
- digital (60, 76, 1048575)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- (4, 12, 100)-net in base 27, using
(72, 88, large)-Net over F27 — Digital
Digital (72, 88, large)-net over F27, using
- 3 times m-reduction [i] based on digital (72, 91, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2791, large, F27, 19) (dual of [large, large−91, 20]-code), using
(72, 88, large)-Net in Base 27 — Upper bound on s
There is no (72, 88, large)-net in base 27, because
- 14 times m-reduction [i] would yield (72, 74, large)-net in base 27, but