Best Known (107, 107+25, s)-Nets in Base 8
(107, 107+25, 21847)-Net over F8 — Constructive and digital
Digital (107, 132, 21847)-net over F8, using
- 81 times duplication [i] based on digital (106, 131, 21847)-net over F8, using
- net defined by OOA [i] based on linear OOA(8131, 21847, F8, 25, 25) (dual of [(21847, 25), 546044, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8131, 262165, F8, 25) (dual of [262165, 262034, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 262166, F8, 25) (dual of [262166, 262035, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(84, 22, F8, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,8)), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8131, 262166, F8, 25) (dual of [262166, 262035, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8131, 262165, F8, 25) (dual of [262165, 262034, 26]-code), using
- net defined by OOA [i] based on linear OOA(8131, 21847, F8, 25, 25) (dual of [(21847, 25), 546044, 26]-NRT-code), using
(107, 107+25, 187505)-Net over F8 — Digital
Digital (107, 132, 187505)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8132, 187505, F8, 25) (dual of [187505, 187373, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8132, 262168, F8, 25) (dual of [262168, 262036, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(19) [i] based on
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(84, 23, F8, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,8)), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8132, 262168, F8, 25) (dual of [262168, 262036, 26]-code), using
(107, 107+25, large)-Net in Base 8 — Upper bound on s
There is no (107, 132, large)-net in base 8, because
- 23 times m-reduction [i] would yield (107, 109, large)-net in base 8, but