Best Known (249−118, 249, s)-Nets in Base 4
(249−118, 249, 130)-Net over F4 — Constructive and digital
Digital (131, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(249−118, 249, 207)-Net over F4 — Digital
Digital (131, 249, 207)-net over F4, using
(249−118, 249, 2594)-Net in Base 4 — Upper bound on s
There is no (131, 249, 2595)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 822314 666662 262376 699267 317350 703212 088993 104223 333050 480978 176679 504503 669190 478201 940643 461627 672277 204728 837743 744111 210711 790636 620342 188775 299840 > 4249 [i]