Best Known (49−25, 49, s)-Nets in Base 3
(49−25, 49, 32)-Net over F3 — Constructive and digital
Digital (24, 49, 32)-net over F3, using
- t-expansion [i] based on digital (21, 49, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(49−25, 49, 33)-Net over F3 — Digital
Digital (24, 49, 33)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(349, 33, F3, 4, 25) (dual of [(33, 4), 83, 26]-NRT-code), using
- 31 times duplication [i] based on linear OOA(348, 33, F3, 4, 25) (dual of [(33, 4), 84, 26]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(344, 32, F3, 4, 25) (dual of [(32, 4), 84, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,102P) [i] based on function field F/F3 with g(F) = 19 and N(F) ≥ 32, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(344, 32, F3, 4, 25) (dual of [(32, 4), 84, 26]-NRT-code), using
- 31 times duplication [i] based on linear OOA(348, 33, F3, 4, 25) (dual of [(33, 4), 84, 26]-NRT-code), using
(49−25, 49, 202)-Net in Base 3 — Upper bound on s
There is no (24, 49, 203)-net in base 3, because
- 1 times m-reduction [i] would yield (24, 48, 203)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 79987 991938 255049 631433 > 348 [i]