Best Known (118, 118+107, s)-Nets in Base 4
(118, 118+107, 130)-Net over F4 — Constructive and digital
Digital (118, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 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
(118, 118+107, 187)-Net over F4 — Digital
Digital (118, 225, 187)-net over F4, using
(118, 118+107, 2362)-Net in Base 4 — Upper bound on s
There is no (118, 225, 2363)-net in base 4, because
- 1 times m-reduction [i] would yield (118, 224, 2363)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 739 053746 921449 758661 614221 182208 966378 997103 136618 783773 425457 613917 683407 499571 084863 545573 365541 575392 371523 984551 814387 303835 733860 > 4224 [i]