Best Known (116, 142, s)-Nets in Base 3
(116, 142, 688)-Net over F3 — Constructive and digital
Digital (116, 142, 688)-net over F3, using
- t-expansion [i] based on digital (115, 142, 688)-net over F3, using
- 2 times m-reduction [i] based on digital (115, 144, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 36, 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, 36, 172)-net over F81, using
- 2 times m-reduction [i] based on digital (115, 144, 688)-net over F3, using
(116, 142, 3291)-Net over F3 — Digital
Digital (116, 142, 3291)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3142, 3291, F3, 2, 26) (dual of [(3291, 2), 6440, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3142, 6582, F3, 26) (dual of [6582, 6440, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3142, 6583, F3, 26) (dual of [6583, 6441, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(22) ⊂ Ce(21) [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(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(34, 21, F3, 2) (dual of [21, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3142, 6583, F3, 26) (dual of [6583, 6441, 27]-code), using
- OOA 2-folding [i] based on linear OA(3142, 6582, F3, 26) (dual of [6582, 6440, 27]-code), using
(116, 142, 461313)-Net in Base 3 — Upper bound on s
There is no (116, 142, 461314)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 56 392176 689840 311959 119380 976423 384380 020002 229563 047799 975453 060685 > 3142 [i]