Best Known (135−20, 135, s)-Nets in Base 8
(135−20, 135, 209743)-Net over F8 — Constructive and digital
Digital (115, 135, 209743)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-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 (5, 15, 28)-net over F8, using
(135−20, 135, 2956724)-Net over F8 — Digital
Digital (115, 135, 2956724)-net over F8, using
(135−20, 135, large)-Net in Base 8 — Upper bound on s
There is no (115, 135, large)-net in base 8, because
- 18 times m-reduction [i] would yield (115, 117, large)-net in base 8, but