Best Known (118, 118+103, s)-Nets in Base 4
(118, 118+103, 130)-Net over F4 — Constructive and digital
Digital (118, 221, 130)-net over F4, using
- t-expansion [i] based on digital (105, 221, 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+103, 196)-Net over F4 — Digital
Digital (118, 221, 196)-net over F4, using
(118, 118+103, 2575)-Net in Base 4 — Upper bound on s
There is no (118, 221, 2576)-net in base 4, because
- 1 times m-reduction [i] would yield (118, 220, 2576)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 863042 630691 020584 139307 524004 130407 065268 478425 217813 023847 620397 403414 483869 149272 000338 201180 155026 774622 949754 365507 137325 835360 > 4220 [i]