Best Known (150−20, 150, s)-Nets in Base 8
(150−20, 150, 838884)-Net over F8 — Constructive and digital
Digital (130, 150, 838884)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (117, 137, 838860)-net over F8, using
- net defined by OOA [i] based on linear OOA(8137, 838860, F8, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8137, 8388600, F8, 20) (dual of [8388600, 8388463, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8137, 8388600, F8, 20) (dual of [8388600, 8388463, 21]-code), using
- net defined by OOA [i] based on linear OOA(8137, 838860, F8, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
- digital (3, 13, 24)-net over F8, using
(150−20, 150, large)-Net over F8 — Digital
Digital (130, 150, large)-net over F8, using
- 84 times duplication [i] based on digital (126, 146, large)-net over F8, using
- t-expansion [i] based on digital (125, 146, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8146, large, F8, 21) (dual of [large, large−146, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8146, large, F8, 21) (dual of [large, large−146, 22]-code), using
- t-expansion [i] based on digital (125, 146, large)-net over F8, using
(150−20, 150, large)-Net in Base 8 — Upper bound on s
There is no (130, 150, large)-net in base 8, because
- 18 times m-reduction [i] would yield (130, 132, large)-net in base 8, but