Best Known (24, 24+29, s)-Nets in Base 49
(24, 24+29, 344)-Net over F49 — Constructive and digital
Digital (24, 53, 344)-net over F49, using
- t-expansion [i] based on digital (21, 53, 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
(24, 24+29, 388)-Net over F49 — Digital
Digital (24, 53, 388)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4953, 388, F49, 29) (dual of [388, 335, 30]-code), using
- 41 step Varšamov–Edel lengthening with (ri) = (2, 8 times 0, 1, 31 times 0) [i] based on linear OA(4950, 344, F49, 29) (dual of [344, 294, 30]-code), using
- extended algebraic-geometric code AGe(F,314P) [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,314P) [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- 41 step Varšamov–Edel lengthening with (ri) = (2, 8 times 0, 1, 31 times 0) [i] based on linear OA(4950, 344, F49, 29) (dual of [344, 294, 30]-code), using
(24, 24+29, 238822)-Net in Base 49 — Upper bound on s
There is no (24, 53, 238823)-net in base 49, because
- 1 times m-reduction [i] would yield (24, 52, 238823)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 7766 189212 377612 134187 262020 953696 817277 171412 232787 731438 614982 024538 064447 986266 284641 > 4952 [i]