Best Known (107, 107+109, s)-Nets in Base 4
(107, 107+109, 130)-Net over F4 — Constructive and digital
Digital (107, 216, 130)-net over F4, using
- t-expansion [i] based on digital (105, 216, 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
(107, 107+109, 149)-Net over F4 — Digital
Digital (107, 216, 149)-net over F4, using
(107, 107+109, 1699)-Net in Base 4 — Upper bound on s
There is no (107, 216, 1700)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 215, 1700)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2790 630701 608322 368908 337368 886022 784307 949149 442481 377457 467545 258652 113032 546272 514482 765883 622682 425800 727293 483093 732465 831328 > 4215 [i]