Best Known (113, 113+84, s)-Nets in Base 4
(113, 113+84, 130)-Net over F4 — Constructive and digital
Digital (113, 197, 130)-net over F4, using
- t-expansion [i] based on digital (105, 197, 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
(113, 113+84, 235)-Net over F4 — Digital
Digital (113, 197, 235)-net over F4, using
(113, 113+84, 3635)-Net in Base 4 — Upper bound on s
There is no (113, 197, 3636)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 40668 636418 037592 898488 649385 594083 534872 120508 874981 876260 694486 409786 471442 292534 507640 258921 962639 223318 177534 029470 > 4197 [i]