MinT - Best Known (224−107, 224, s)-Nets in Base 4

Best Known (224−107, 224, s)-Nets in Base 4

(224−107, 224, 130)-Net over F₄ — Constructive and digital

Digital (117, 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]

(224−107, 224, 183)-Net over F₄ — Digital

Digital (117, 224, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−107, 224, 2300)-Net in Base 4 — Upper bound on s

There is no (117, 224, 2301)-net in base 4, because

1 times m-reduction [i] would yield (117, 223, 2301)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 185 257897 519093 249883 223019 294058 091369 651717 916224 393355 345577 215187 216754 307471 930216 814832 537228 863575 523247 998193 995829 975070 790692 > 4²²³ [i]