Best Known (110, 130, s)-Nets in Base 8
(110, 130, 209724)-Net over F8 — Constructive and digital
Digital (110, 130, 209724)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (100, 120, 209715)-net over F8, using
- net defined by OOA [i] based on linear OOA(8120, 209715, F8, 20, 20) (dual of [(209715, 20), 4194180, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8120, 2097150, F8, 20) (dual of [2097150, 2097030, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8120, 2097150, F8, 20) (dual of [2097150, 2097030, 21]-code), using
- net defined by OOA [i] based on linear OOA(8120, 209715, F8, 20, 20) (dual of [(209715, 20), 4194180, 21]-NRT-code), using
- digital (0, 10, 9)-net over F8, using
(110, 130, 2097204)-Net over F8 — Digital
Digital (110, 130, 2097204)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8130, 2097204, F8, 20) (dual of [2097204, 2097074, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
(110, 130, large)-Net in Base 8 — Upper bound on s
There is no (110, 130, large)-net in base 8, because
- 18 times m-reduction [i] would yield (110, 112, large)-net in base 8, but