Best Known (144, 144+26, s)-Nets in Base 8
(144, 144+26, 161336)-Net over F8 — Constructive and digital
Digital (144, 170, 161336)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (129, 155, 161319)-net over F8, using
- net defined by OOA [i] based on linear OOA(8155, 161319, F8, 26, 26) (dual of [(161319, 26), 4194139, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8155, 2097147, F8, 26) (dual of [2097147, 2096992, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8155, 2097147, F8, 26) (dual of [2097147, 2096992, 27]-code), using
- net defined by OOA [i] based on linear OOA(8155, 161319, F8, 26, 26) (dual of [(161319, 26), 4194139, 27]-NRT-code), using
- digital (2, 15, 17)-net over F8, using
(144, 144+26, 2097223)-Net over F8 — Digital
Digital (144, 170, 2097223)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8170, 2097223, F8, 26) (dual of [2097223, 2097053, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(16) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(815, 71, F8, 8) (dual of [71, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(815, 73, F8, 8) (dual of [73, 58, 9]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(815, 73, F8, 8) (dual of [73, 58, 9]-code), using
- construction X applied to Ce(25) ⊂ Ce(16) [i] based on
(144, 144+26, large)-Net in Base 8 — Upper bound on s
There is no (144, 170, large)-net in base 8, because
- 24 times m-reduction [i] would yield (144, 146, large)-net in base 8, but