Best Known (126, 157, s)-Nets in Base 8
(126, 157, 2213)-Net over F8 — Constructive and digital
Digital (126, 157, 2213)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 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 (106, 137, 2185)-net over F8, using
- net defined by OOA [i] based on linear OOA(8137, 2185, F8, 31, 31) (dual of [(2185, 31), 67598, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8137, 32776, F8, 31) (dual of [32776, 32639, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 32779, F8, 31) (dual of [32779, 32642, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(8137, 32779, F8, 31) (dual of [32779, 32642, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8137, 32776, F8, 31) (dual of [32776, 32639, 32]-code), using
- net defined by OOA [i] based on linear OOA(8137, 2185, F8, 31, 31) (dual of [(2185, 31), 67598, 32]-NRT-code), using
- digital (5, 20, 28)-net over F8, using
(126, 157, 4369)-Net in Base 8 — Constructive
(126, 157, 4369)-net in base 8, using
- 81 times duplication [i] based on (125, 156, 4369)-net in base 8, using
- base change [i] based on digital (86, 117, 4369)-net over F16, using
- net defined by OOA [i] based on linear OOA(16117, 4369, F16, 31, 31) (dual of [(4369, 31), 135322, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using
- net defined by OOA [i] based on linear OOA(16117, 4369, F16, 31, 31) (dual of [(4369, 31), 135322, 32]-NRT-code), using
- base change [i] based on digital (86, 117, 4369)-net over F16, using
(126, 157, 91608)-Net over F8 — Digital
Digital (126, 157, 91608)-net over F8, using
(126, 157, large)-Net in Base 8 — Upper bound on s
There is no (126, 157, large)-net in base 8, because
- 29 times m-reduction [i] would yield (126, 128, large)-net in base 8, but