Best Known (43−22, 43, s)-Nets in Base 49
(43−22, 43, 344)-Net over F49 — Constructive and digital
Digital (21, 43, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
(43−22, 43, 801)-Net over F49 — Digital
Digital (21, 43, 801)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4943, 801, F49, 3, 22) (dual of [(801, 3), 2360, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4943, 2403, F49, 22) (dual of [2403, 2360, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4943, 2401, F49, 22) (dual of [2401, 2358, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4941, 2401, F49, 21) (dual of [2401, 2360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- OOA 3-folding [i] based on linear OA(4943, 2403, F49, 22) (dual of [2403, 2360, 23]-code), using
(43−22, 43, 413902)-Net in Base 49 — Upper bound on s
There is no (21, 43, 413903)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 4 769167 365950 247802 719272 682316 237084 678280 162504 484194 430776 980602 131185 > 4943 [i]