Best Known (107, 107+75, s)-Nets in Base 4
(107, 107+75, 130)-Net over F4 — Constructive and digital
Digital (107, 182, 130)-net over F4, using
- t-expansion [i] based on digital (105, 182, 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+75, 244)-Net over F4 — Digital
Digital (107, 182, 244)-net over F4, using
(107, 107+75, 4275)-Net in Base 4 — Upper bound on s
There is no (107, 182, 4276)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 181, 4276)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9 471693 308016 337720 747525 204146 962316 614142 686399 882751 694097 742585 969092 213644 908671 626345 429478 099839 063132 > 4181 [i]