Best Known (22, 22+27, s)-Nets in Base 49
(22, 22+27, 344)-Net over F49 — Constructive and digital
Digital (22, 49, 344)-net over F49, using
- t-expansion [i] based on digital (21, 49, 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
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(22, 22+27, 356)-Net over F49 — Digital
Digital (22, 49, 356)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4949, 356, F49, 27) (dual of [356, 307, 28]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(4948, 344, F49, 27) (dual of [344, 296, 28]-code), using
- extended algebraic-geometric code AGe(F,316P) [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- extended algebraic-geometric code AGe(F,316P) [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(4948, 344, F49, 27) (dual of [344, 296, 28]-code), using
(22, 22+27, 205530)-Net in Base 49 — Upper bound on s
There is no (22, 49, 205531)-net in base 49, because
- 1 times m-reduction [i] would yield (22, 48, 205531)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 1347 204053 405913 011231 245430 700875 574139 912482 019525 245192 482586 855248 813789 348305 > 4948 [i]