Best Known (114, 114+26, s)-Nets in Base 3
(114, 114+26, 688)-Net over F3 — Constructive and digital
Digital (114, 140, 688)-net over F3, using
- t-expansion [i] based on digital (112, 140, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 35, 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, 35, 172)-net over F81, using
(114, 114+26, 3287)-Net over F3 — Digital
Digital (114, 140, 3287)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3140, 3287, F3, 2, 26) (dual of [(3287, 2), 6434, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3140, 6574, F3, 26) (dual of [6574, 6434, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(3140, 6574, F3, 26) (dual of [6574, 6434, 27]-code), using
(114, 114+26, 389575)-Net in Base 3 — Upper bound on s
There is no (114, 140, 389576)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 265984 244806 503254 644311 502786 107442 104126 738991 132168 902809 040273 > 3140 [i]