Best Known (108, 132, s)-Nets in Base 8
(108, 132, 21847)-Net over F8 — Constructive and digital
Digital (108, 132, 21847)-net over F8, using
- 81 times duplication [i] based on digital (107, 131, 21847)-net over F8, using
- t-expansion [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
- t-expansion [i] based on digital (106, 131, 21847)-net over F8, using
(108, 132, 262174)-Net over F8 — Digital
Digital (108, 132, 262174)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8132, 262174, F8, 24) (dual of [262174, 262042, 25]-code), using
- construction XX applied to Ce(24) ⊂ Ce(19) ⊂ Ce(18) [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(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(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(84, 29, F8, 3) (dual of [29, 25, 4]-code or 29-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(19) ⊂ Ce(18) [i] based on
(108, 132, large)-Net in Base 8 — Upper bound on s
There is no (108, 132, large)-net in base 8, because
- 22 times m-reduction [i] would yield (108, 110, large)-net in base 8, but