Best Known (117−26, 117, s)-Nets in Base 2
(117−26, 117, 152)-Net over F2 — Constructive and digital
Digital (91, 117, 152)-net over F2, using
- 21 times duplication [i] based on digital (90, 116, 152)-net over F2, using
- trace code for nets [i] based on digital (3, 29, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- trace code for nets [i] based on digital (3, 29, 38)-net over F16, using
(117−26, 117, 255)-Net over F2 — Digital
Digital (91, 117, 255)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, 255, F2, 2, 26) (dual of [(255, 2), 393, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2117, 510, F2, 26) (dual of [510, 393, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2117, 511, F2, 26) (dual of [511, 394, 27]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2117, 511, F2, 26) (dual of [511, 394, 27]-code), using
- OOA 2-folding [i] based on linear OA(2117, 510, F2, 26) (dual of [510, 393, 27]-code), using
(117−26, 117, 2882)-Net in Base 2 — Upper bound on s
There is no (91, 117, 2883)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 166217 637382 138437 594028 200340 888064 > 2117 [i]