Best Known (97, 97+18, s)-Nets in Base 2
(97, 97+18, 480)-Net over F2 — Constructive and digital
Digital (97, 115, 480)-net over F2, using
- 21 times duplication [i] based on digital (96, 114, 480)-net over F2, using
- trace code for nets [i] based on digital (1, 19, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 19, 80)-net over F64, using
(97, 97+18, 1375)-Net over F2 — Digital
Digital (97, 115, 1375)-net over F2, using
- 21 times duplication [i] based on digital (96, 114, 1375)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2114, 1375, F2, 3, 18) (dual of [(1375, 3), 4011, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2114, 4125, F2, 18) (dual of [4125, 4011, 19]-code), using
- 1 times truncation [i] based on linear OA(2115, 4126, F2, 19) (dual of [4126, 4011, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-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(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2115, 4126, F2, 19) (dual of [4126, 4011, 20]-code), using
- OOA 3-folding [i] based on linear OA(2114, 4125, F2, 18) (dual of [4125, 4011, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2114, 1375, F2, 3, 18) (dual of [(1375, 3), 4011, 19]-NRT-code), using
(97, 97+18, 29110)-Net in Base 2 — Upper bound on s
There is no (97, 115, 29111)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 41542 805421 741635 387003 817553 754624 > 2115 [i]