Best Known (91−20, 91, s)-Nets in Base 2
(91−20, 91, 138)-Net over F2 — Constructive and digital
Digital (71, 91, 138)-net over F2, using
- 21 times duplication [i] based on digital (70, 90, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 30, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 30, 46)-net over F8, using
(91−20, 91, 247)-Net over F2 — Digital
Digital (71, 91, 247)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(291, 247, F2, 2, 20) (dual of [(247, 2), 403, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(291, 260, F2, 2, 20) (dual of [(260, 2), 429, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(291, 520, F2, 20) (dual of [520, 429, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(291, 521, F2, 20) (dual of [521, 430, 21]-code), using
- 1 times truncation [i] based on linear OA(292, 522, F2, 21) (dual of [522, 430, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(291, 512, F2, 21) (dual of [512, 421, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(282, 512, F2, 19) (dual of [512, 430, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(292, 522, F2, 21) (dual of [522, 430, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(291, 521, F2, 20) (dual of [521, 430, 21]-code), using
- OOA 2-folding [i] based on linear OA(291, 520, F2, 20) (dual of [520, 429, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(291, 260, F2, 2, 20) (dual of [(260, 2), 429, 21]-NRT-code), using
(91−20, 91, 2470)-Net in Base 2 — Upper bound on s
There is no (71, 91, 2471)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2479 183500 489497 956187 163036 > 291 [i]