MinT - Best Known (113, 113+107, s)-Nets in Base 4

Best Known (113, 113+107, s)-Nets in Base 4

(113, 113+107, 130)-Net over F₄ — Constructive and digital

Digital (113, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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]

(113, 113+107, 170)-Net over F₄ — Digital

Digital (113, 220, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+107, 2067)-Net in Base 4 — Upper bound on s

There is no (113, 220, 2068)-net in base 4, because

1 times m-reduction [i] would yield (113, 219, 2068)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 720977 868262 414843 112145 349314 363051 404474 920367 265762 831063 331852 637322 572363 390832 015231 167607 264827 390659 847283 365129 023693 780480 > 4²¹⁹ [i]