Best Known (74−16, 74, s)-Nets in Base 27
(74−16, 74, 66498)-Net over F27 — Constructive and digital
Digital (58, 74, 66498)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 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 (45, 61, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
- net defined by OOA [i] based on linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code), using
- digital (5, 13, 68)-net over F27, using
(74−16, 74, 66531)-Net in Base 27 — Constructive
(58, 74, 66531)-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 (46, 62, 66431)-net over F27, using
- net defined by OOA [i] based on linear OOA(2762, 66431, F27, 16, 16) (dual of [(66431, 16), 1062834, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2762, 531448, F27, 16) (dual of [531448, 531386, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2762, 531450, F27, 16) (dual of [531450, 531388, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2753, 531441, F27, 14) (dual of [531441, 531388, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2762, 531450, F27, 16) (dual of [531450, 531388, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2762, 531448, F27, 16) (dual of [531448, 531386, 17]-code), using
- net defined by OOA [i] based on linear OOA(2762, 66431, F27, 16, 16) (dual of [(66431, 16), 1062834, 17]-NRT-code), using
- (4, 12, 100)-net in base 27, using
(74−16, 74, 2845699)-Net over F27 — Digital
Digital (58, 74, 2845699)-net over F27, using
(74−16, 74, large)-Net in Base 27 — Upper bound on s
There is no (58, 74, large)-net in base 27, because
- 14 times m-reduction [i] would yield (58, 60, large)-net in base 27, but