Best Known (105, 128, s)-Nets in Base 2
(105, 128, 265)-Net over F2 — Constructive and digital
Digital (105, 128, 265)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- digital (93, 116, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 29, 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, 29, 65)-net over F16, using
- digital (1, 12, 5)-net over F2, using
(105, 128, 692)-Net over F2 — Digital
Digital (105, 128, 692)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2128, 692, F2, 3, 23) (dual of [(692, 3), 1948, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [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]
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- OOA 3-folding [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
(105, 128, 14657)-Net in Base 2 — Upper bound on s
There is no (105, 128, 14658)-net in base 2, because
- 1 times m-reduction [i] would yield (105, 127, 14658)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 170 167020 281909 318572 337279 565088 134592 > 2127 [i]