Best Known (23, 62, s)-Nets in Base 128
(23, 62, 342)-Net over F128 — Constructive and digital
Digital (23, 62, 342)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 20, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (3, 42, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (1, 20, 150)-net over F128, using
(23, 62, 389)-Net over F128 — Digital
Digital (23, 62, 389)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12862, 389, F128, 4, 39) (dual of [(389, 4), 1494, 40]-NRT-code), using
- construction X applied to AG(4;F,1500P) ⊂ AG(4;F,1509P) [i] based on
- linear OOA(12854, 385, F128, 4, 39) (dual of [(385, 4), 1486, 40]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1500P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- linear OOA(12845, 385, F128, 4, 30) (dual of [(385, 4), 1495, 31]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1509P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386 (see above)
- linear OOA(1288, 4, F128, 4, 8) (dual of [(4, 4), 8, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1288, 128, F128, 4, 8) (dual of [(128, 4), 504, 9]-NRT-code), using
- Reed–Solomon NRT-code RS(4;504,128) [i]
- discarding factors / shortening the dual code based on linear OOA(1288, 128, F128, 4, 8) (dual of [(128, 4), 504, 9]-NRT-code), using
- construction X applied to AG(4;F,1500P) ⊂ AG(4;F,1509P) [i] based on
(23, 62, 513)-Net in Base 128
(23, 62, 513)-net in base 128, using
- t-expansion [i] based on (17, 62, 513)-net in base 128, using
- 10 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- 10 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(23, 62, 363625)-Net in Base 128 — Upper bound on s
There is no (23, 62, 363626)-net in base 128, because
- 1 times m-reduction [i] would yield (23, 61, 363626)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 346 599031 214666 682262 809277 476799 237746 204380 959167 095237 164067 784230 894309 324207 424943 846014 578217 045095 063582 545667 057468 400792 > 12861 [i]