Best Known (95, 95+155, s)-Nets in Base 4
(95, 95+155, 104)-Net over F4 — Constructive and digital
Digital (95, 250, 104)-net over F4, using
- t-expansion [i] based on digital (73, 250, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(95, 95+155, 144)-Net over F4 — Digital
Digital (95, 250, 144)-net over F4, using
- t-expansion [i] based on digital (91, 250, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(95, 95+155, 807)-Net in Base 4 — Upper bound on s
There is no (95, 250, 808)-net in base 4, because
- 1 times m-reduction [i] would yield (95, 249, 808)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 827304 795821 221480 067509 546348 747850 725648 663180 750235 155422 726746 368098 803052 306770 856431 091094 424670 238247 579759 132631 344765 857600 417233 668203 521520 > 4249 [i]