Best Known (35, 35+36, s)-Nets in Base 128
(35, 35+36, 910)-Net over F128 — Constructive and digital
Digital (35, 71, 910)-net over F128, using
- net defined by OOA [i] based on linear OOA(12871, 910, F128, 36, 36) (dual of [(910, 36), 32689, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(12871, 16380, F128, 36) (dual of [16380, 16309, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(12871, 16380, F128, 36) (dual of [16380, 16309, 37]-code), using
(35, 35+36, 3489)-Net over F128 — Digital
Digital (35, 71, 3489)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12871, 3489, F128, 4, 36) (dual of [(3489, 4), 13885, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12871, 4096, F128, 4, 36) (dual of [(4096, 4), 16313, 37]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- OOA 4-folding [i] based on linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(12871, 4096, F128, 4, 36) (dual of [(4096, 4), 16313, 37]-NRT-code), using
(35, 35+36, large)-Net in Base 128 — Upper bound on s
There is no (35, 71, large)-net in base 128, because
- 34 times m-reduction [i] would yield (35, 37, large)-net in base 128, but