Best Known (94, 114, s)-Nets in Base 3
(94, 114, 688)-Net over F3 — Constructive and digital
Digital (94, 114, 688)-net over F3, using
- 2 times m-reduction [i] based on digital (94, 116, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
(94, 114, 3719)-Net over F3 — Digital
Digital (94, 114, 3719)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3114, 3719, F3, 20) (dual of [3719, 3605, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3114, 6596, F3, 20) (dual of [6596, 6482, 21]-code), using
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(36, 32, F3, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
- construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3114, 6596, F3, 20) (dual of [6596, 6482, 21]-code), using
(94, 114, 622475)-Net in Base 3 — Upper bound on s
There is no (94, 114, 622476)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 465070 354922 885119 097773 484684 045841 923535 276058 316649 > 3114 [i]