Best Known (78, 94, s)-Nets in Base 27
(78, 94, 1048760)-Net over F27 — Constructive and digital
Digital (78, 94, 1048760)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 18, 185)-net over F27, using
- net defined by OOA [i] based on linear OOA(2718, 185, F27, 8, 8) (dual of [(185, 8), 1462, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2718, 740, F27, 8) (dual of [740, 722, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(2715, 729, F27, 8) (dual of [729, 714, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(277, 729, F27, 4) (dual of [729, 722, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(273, 11, F27, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,27) or 11-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- OA 4-folding and stacking [i] based on linear OA(2718, 740, F27, 8) (dual of [740, 722, 9]-code), using
- net defined by OOA [i] based on linear OOA(2718, 185, F27, 8, 8) (dual of [(185, 8), 1462, 9]-NRT-code), 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 (10, 18, 185)-net over F27, using
(78, 94, 1048775)-Net in Base 27 — Constructive
(78, 94, 1048775)-net in base 27, using
- (u, u+v)-construction [i] based on
- (10, 18, 200)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- 1 times truncation [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
- (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 (2, 6, 351)-net over F27, using
- (u, u+v)-construction [i] based on
- 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
- (10, 18, 200)-net in base 27, using
(78, 94, large)-Net over F27 — Digital
Digital (78, 94, large)-net over F27, using
- t-expansion [i] based on digital (76, 94, large)-net over F27, using
- 2 times m-reduction [i] based on digital (76, 96, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- 2 times m-reduction [i] based on digital (76, 96, large)-net over F27, using
(78, 94, large)-Net in Base 27 — Upper bound on s
There is no (78, 94, large)-net in base 27, because
- 14 times m-reduction [i] would yield (78, 80, large)-net in base 27, but