Best Known (125, 125+97, s)-Nets in Base 4
(125, 125+97, 130)-Net over F4 — Constructive and digital
Digital (125, 222, 130)-net over F4, using
- t-expansion [i] based on digital (105, 222, 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
(125, 125+97, 241)-Net over F4 — Digital
Digital (125, 222, 241)-net over F4, using
(125, 125+97, 3655)-Net in Base 4 — Upper bound on s
There is no (125, 222, 3656)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 221, 3656)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 358443 097855 189410 924027 426351 117063 831836 864080 824641 689500 661203 016162 849255 296101 683790 829594 915587 747555 329017 928273 837888 206092 > 4221 [i]