Best Known (99, 121, s)-Nets in Base 2
(99, 121, 260)-Net over F2 — Constructive and digital
Digital (99, 121, 260)-net over F2, using
- 3 times m-reduction [i] based on digital (99, 124, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 31, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 31, 65)-net over F16, using
(99, 121, 682)-Net over F2 — Digital
Digital (99, 121, 682)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2121, 682, F2, 3, 22) (dual of [(682, 3), 1925, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2121, 2046, F2, 22) (dual of [2046, 1925, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2121, 2047, F2, 22) (dual of [2047, 1926, 23]-code), using
- 1 times truncation [i] based on linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2121, 2047, F2, 22) (dual of [2047, 1926, 23]-code), using
- OOA 3-folding [i] based on linear OA(2121, 2046, F2, 22) (dual of [2046, 1925, 23]-code), using
(99, 121, 10038)-Net in Base 2 — Upper bound on s
There is no (99, 121, 10039)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2 660980 407942 443395 066468 585734 282100 > 2121 [i]