Best Known (125, 155, s)-Nets in Base 8
(125, 155, 2229)-Net over F8 — Constructive and digital
Digital (125, 155, 2229)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (101, 131, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- digital (9, 24, 45)-net over F8, using
(125, 155, 4370)-Net in Base 8 — Constructive
(125, 155, 4370)-net in base 8, using
- 81 times duplication [i] based on (124, 154, 4370)-net in base 8, using
- net defined by OOA [i] based on OOA(8154, 4370, S8, 30, 30), using
- OA 15-folding and stacking [i] based on OA(8154, 65550, S8, 30), using
- discarding parts of the base [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- discarding parts of the base [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- OA 15-folding and stacking [i] based on OA(8154, 65550, S8, 30), using
- net defined by OOA [i] based on OOA(8154, 4370, S8, 30, 30), using
(125, 155, 111928)-Net over F8 — Digital
Digital (125, 155, 111928)-net over F8, using
(125, 155, large)-Net in Base 8 — Upper bound on s
There is no (125, 155, large)-net in base 8, because
- 28 times m-reduction [i] would yield (125, 127, large)-net in base 8, but