MinT - Best Known (110, 203, s)-Nets in Base 4

Best Known (110, 203, s)-Nets in Base 4

(110, 203, 130)-Net over F₄ — Constructive and digital

Digital (110, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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, 203, 192)-Net over F₄ — Digital

Digital (110, 203, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 203, 2604)-Net in Base 4 — Upper bound on s

There is no (110, 203, 2605)-net in base 4, because

1 times m-reduction [i] would yield (110, 202, 2605)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 750508 201772 814935 948306 866957 080343 425710 900101 350014 630548 494380 741700 860239 756240 191747 655788 812653 004914 309114 041776 > 4²⁰² [i]