Best Known (100, 121, s)-Nets in Base 2
(100, 121, 409)-Net over F2 — Constructive and digital
Digital (100, 121, 409)-net over F2, using
- net defined by OOA [i] based on linear OOA(2121, 409, F2, 21, 21) (dual of [(409, 21), 8468, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2121, 4091, F2, 21) (dual of [4091, 3970, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2121, 4091, F2, 21) (dual of [4091, 3970, 22]-code), using
(100, 121, 1024)-Net over F2 — Digital
Digital (100, 121, 1024)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2121, 1024, F2, 4, 21) (dual of [(1024, 4), 3975, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 4-folding [i] based on linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using
(100, 121, 18535)-Net in Base 2 — Upper bound on s
There is no (100, 121, 18536)-net in base 2, because
- 1 times m-reduction [i] would yield (100, 120, 18536)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 329817 298884 290513 640167 875262 974268 > 2120 [i]