MinT - Best Known (114, 114+85, s)-Nets in Base 4

Best Known (114, 114+85, s)-Nets in Base 4

(114, 114+85, 130)-Net over F₄ — Constructive and digital

Digital (114, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 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]

(114, 114+85, 236)-Net over F₄ — Digital

Digital (114, 199, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+85, 3758)-Net in Base 4 — Upper bound on s

There is no (114, 199, 3759)-net in base 4, because

1 times m-reduction [i] would yield (114, 198, 3759)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 162376 374294 819010 382705 459694 330930 550205 667725 110844 010351 336138 187208 239993 540467 042839 777015 489195 850389 469678 432325 > 4¹⁹⁸ [i]