MinT - Best Known (214−95, 214, s)-Nets in Base 4

Best Known (214−95, 214, s)-Nets in Base 4

(214−95, 214, 130)-Net over F₄ — Constructive and digital

Digital (119, 214, 130)-net over F₄, using

t-expansion [i] based on digital (105, 214, 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]

(214−95, 214, 222)-Net over F₄ — Digital

Digital (119, 214, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−95, 214, 3238)-Net in Base 4 — Upper bound on s

There is no (119, 214, 3239)-net in base 4, because

1 times m-reduction [i] would yield (119, 213, 3239)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 174 781493 988128 945094 249769 433386 356232 923106 344927 157235 833211 875051 430013 386590 514512 516686 445792 799895 562149 263044 894963 739200 > 4²¹³ [i]