MinT - Best Known (110, 110+87, s)-Nets in Base 4

Best Known (110, 110+87, s)-Nets in Base 4

(110, 110+87, 130)-Net over F₄ — Constructive and digital

Digital (110, 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
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(110, 110+87, 210)-Net over F₄ — Digital

Digital (110, 197, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+87, 3088)-Net in Base 4 — Upper bound on s

There is no (110, 197, 3089)-net in base 4, because

1 times m-reduction [i] would yield (110, 196, 3089)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10202 914153 843077 784217 785565 179530 774690 888659 236510 708588 412460 027185 016466 053973 898162 132520 199344 919864 223761 400320 > 4¹⁹⁶ [i]