MinT - Best Known (224−105, 224, s)-Nets in Base 4

Best Known (224−105, 224, s)-Nets in Base 4

(224−105, 224, 130)-Net over F₄ — Constructive and digital

Digital (119, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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]

(224−105, 224, 195)-Net over F₄ — Digital

Digital (119, 224, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−105, 224, 2531)-Net in Base 4 — Upper bound on s

There is no (119, 224, 2532)-net in base 4, because

1 times m-reduction [i] would yield (119, 223, 2532)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 182 071121 563792 681821 131846 608035 436923 342450 332424 471958 885102 180561 119123 469715 721618 388286 477725 950363 909369 990386 946209 888317 510000 > 4²²³ [i]