Best Known (78, 94, s)-Nets in Base 3
(78, 94, 2462)-Net over F3 — Constructive and digital
Digital (78, 94, 2462)-net over F3, using
- net defined by OOA [i] based on linear OOA(394, 2462, F3, 16, 16) (dual of [(2462, 16), 39298, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(394, 19696, F3, 16) (dual of [19696, 19602, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OA 8-folding and stacking [i] based on linear OA(394, 19696, F3, 16) (dual of [19696, 19602, 17]-code), using
(78, 94, 6732)-Net over F3 — Digital
Digital (78, 94, 6732)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(394, 6732, F3, 2, 16) (dual of [(6732, 2), 13370, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 9848, F3, 2, 16) (dual of [(9848, 2), 19602, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(394, 19696, F3, 16) (dual of [19696, 19602, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OOA 2-folding [i] based on linear OA(394, 19696, F3, 16) (dual of [19696, 19602, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(394, 9848, F3, 2, 16) (dual of [(9848, 2), 19602, 17]-NRT-code), using
(78, 94, 760029)-Net in Base 3 — Upper bound on s
There is no (78, 94, 760030)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 706 967757 975177 996704 938282 004163 672475 663953 > 394 [i]